Scope everything to a team, and route alerts by integration key

The core of #4, and what #1 is for: terdut stops being one shared space.
A team owns its incidents, alerts, schedule and integrations; a user sees
exactly the teams they are in. Everything that existed moves into one
Default team and every existing user becomes an owner of it, so the
upgrade is a no-op for the people using it.

Ingestion is the load-bearing half. An alert arrives on a team's
integration key, and the key is both the credential and the routing: it
says that the sender may post, and which team the alerts belong to. That
also closes the unauthenticated webhook -- the old path stays for one
release, deprecated and routed to the oldest team, so an upgrade does not
stop delivering while somebody edits the Alertmanager config.

Scoping is enforced in as few places as possible, because the failure
mode is silent. serveAs loads the caller's memberships once; list queries
carry `team_id = ANY(...)`; and every incident route goes through
incidentIDParam, which now parses the id AND checks the team in the same
call, so a new handler cannot remember the first half and forget the
second. Anything in another team is 404, never 403: whether an incident
exists is that team's business.

Two bugs this found, both of which would have been silent:

  * upsertAlerts decided "is this a new occurrence" by looking up the
    fingerprint alone. Across teams that made team B's first alert look
    like a re-send of team A's, so it opened no incident at all. The
    lookups are keyed on (team_id, fingerprint) now, as the index is.

  * Every uniqueness rule was written for one tenant. Two teams watching
    two clusters legitimately see the same fingerprint, the same
    groupKey, and want somebody on call on the same day; all three
    constraints move to include team_id.

Roles inside a team are separate from the system administrator flag: an
owner configures the team, a member works its incidents, and an admin is
NOT implicitly in every team -- administration is about accounts, not
about reading other people's incidents. An admin can still repair a team
whose owner has left, which is why requireTeamOwner lets them through.

A shift can only be given to somebody in the team. Paging a person who
cannot open the incident is worse than paging nobody.

The UI is updated only as far as keeping it working: it loads the
viewer's teams with the session and uses the first one, since nobody has
a second yet. "On call now" shows every team the viewer is in, named only
when there is more than one, so the common case reads exactly as before.
The team switcher, badges and per-team settings pages are the next step.

Breaking for API clients: the schedule endpoints moved under the team,
and /api/schedule/current returns an array rather than an object or a
404. terdut-tui will need a version for that.

Per-team dead-man configuration is deliberately not here. A heartbeat's
incident already opens in the team whose key received it, which is the
part that matters for isolation; moving the matchers out of env into
per-team rows is a change to how deadman.go is configured rather than to
who sees what.

Claude-Session: https://claude.ai/code/session_01RHPj4ggeFdEjKKfm4SHbD7

README.md

@@ -459,6 +459,16 @@ nobody can delete or demote themselves.
 Endpoints that require the flag answer `403` with
 `{"error":"administrator access required"}`.
 
+**Teams** are the unit of tenancy, and are a separate axis from the administrator
+flag. A team owns its incidents, alerts, schedule and integrations, and a user
+sees exactly the teams they belong to — an administrator is not implicitly in
+every team, because administration is about accounts, not about reading other
+people's incidents. Within a team an **owner** configures it (schedule,
+integrations, membership) and a **member** works its incidents.
+
+Anything belonging to a team you are not in answers `404`, not `403`: whether an
+incident exists is itself something only its team should learn.
+
 | Method | Path | Description |
 |---|---|---|
 | `POST` | `/api/login` | `{"username","password"}` → sets the session cookie, returns `{user, has_password}`. `429` after too many failures |
@@ -487,9 +497,32 @@ on anybody's.
 
 ### Alert ingestion
 
+Alerts arrive on a team's integration key. The key is both the credential and the
+routing: it says that the sender may post, and which team the alerts belong to.
+Create one with `POST /api/teams/{teamID}/integrations`, which returns the key
+and the full URL once and stores only a SHA-256 hash.
+
 | Method | Path | Description |
 |---|---|---|
-| `POST` | `/api/alertmanager/webhook` | Alertmanager v4 webhook receiver (no auth) |
+| `POST` | `/api/integrations/{key}/alertmanager` | Alertmanager v4 webhook receiver for the key's team. `401` for an unknown key |
+| `POST` | `/api/alertmanager/webhook` | **Deprecated, unauthenticated.** The pre-teams receiver, kept for one release so an upgrade does not stop delivering while the Alertmanager config is edited. Routes everything to the oldest team |
+
+The deprecated path is why anything that can reach the port can still open an
+incident. Move senders to a key and it goes away.
+
+### Teams
+
+| Method | Path | Who | Description |
+|---|---|---|---|
+| `GET` | `/api/teams` | any | The caller's own teams, each with their role |
+| `POST` | `/api/teams` | any | Create a team `{"name"}`; the creator becomes its first owner |
+| `DELETE` | `/api/teams/{teamID}` | **owner** | Delete a team and everything under it. `409` while it has open incidents |
+| `GET` | `/api/teams/{teamID}/members` | member | Who is in the team |
+| `POST` | `/api/teams/{teamID}/members` | **owner** | Add a member, or change their role `{"user_id","role"}` |
+| `DELETE` | `/api/teams/{teamID}/members/{userID}` | **owner** | Remove a member. `409` for the last owner |
+| `GET` | `/api/teams/{teamID}/integrations` | member | List integrations. Never returns keys |
+| `POST` | `/api/teams/{teamID}/integrations` | **owner** | Mint an integration `{"name","kind"}` — key and URL shown once |
+| `DELETE` | `/api/teams/{teamID}/integrations/{integrationID}` | **owner** | Revoke an integration |
 
 ### Notifications
 
@@ -676,13 +709,23 @@ unknown" rather than being rejected.
 
 | Method | Path | Description |
 |---|---|---|
-| `POST` | `/api/schedule` | Assign user to dates `{"user_id", "dates":["YYYY-MM-DD",...], "replace"}` — all-or-nothing |
-| `GET` | `/api/schedule` | List entries. Filters: `?from=YYYY-MM-DD`, `?to=YYYY-MM-DD` |
-| `GET` | `/api/schedule/current` | Today's on-call user (UTC), 404 if none |
-| `DELETE` | `/api/schedule/{id}` | Remove schedule entry |
+Each team keeps its own rota, so two teams can have two different people on call
+on the same day. The person taking a shift has to be in the team — paging
+somebody who cannot open the incident is worse than paging nobody.
+
+| Method | Path | Who | Description |
+|---|---|---|---|
+| `POST` | `/api/teams/{teamID}/schedule` | **owner** | Assign user to dates `{"user_id", "dates":["YYYY-MM-DD",...], "replace"}` — all-or-nothing |
+| `GET` | `/api/teams/{teamID}/schedule` | member | List entries. Filters: `?from=YYYY-MM-DD`, `?to=YYYY-MM-DD` |
+| `DELETE` | `/api/teams/{teamID}/schedule/{id}` | **owner** | Remove schedule entry |
+| `GET` | `/api/schedule/current` | any | Who is on call today (UTC) in **every** team the caller is in — one entry per team, `[]` when nobody anywhere |
 
 ### Statistics
 
+Every figure counts the caller's own teams only: a report that counted other
+teams' incidents would leak their volume, and their alert names through the
+top-alerts list, and would not be a number about the reader's work anyway.
+
 All stat endpoints accept optional `?from=YYYY-MM-DD` and `?to=YYYY-MM-DD`, and exclude archived rows to match the default list views. Alert stats filter on `received_at`; incident stats filter on `triggered_at`.
 
 | Method | Path | Description |
@@ -699,6 +742,31 @@ averages over incidents that have actually been acknowledged or resolved, and ar
 
 ---
 
+## Upgrading to teams
+
+Everything that existed before teams moves into one team called **Default**, and
+every existing user becomes an owner of it. The upgrade is a no-op for the
+people using it: the same queue, the same schedule, the same incidents, with a
+name on them.
+
+What changes, and will need attention:
+
+- **Alert ingestion moved.** `POST /api/alertmanager/webhook` still works but is
+  deprecated and unauthenticated, and routes everything to the oldest team. Mint
+  a key with `POST /api/teams/{teamID}/integrations` and point Alertmanager at
+  the URL it returns. The old path goes away in a later release.
+- **The schedule endpoints moved** under `/api/teams/{teamID}/schedule`, and
+  editing the rota is now an owner's job. `GET /api/schedule/current` stayed
+  where it was but now returns an **array** — one entry per team with somebody
+  on call — instead of a single object or a 404. This is a breaking API change
+  for anything that reads it, terdut-tui included.
+- **Uniqueness is per team now.** Two teams can legitimately see the same alert
+  fingerprint, the same Alertmanager groupKey, and put somebody on call on the
+  same date.
+
+Nothing else about an incident changes, and incidents never move between teams:
+an alert belongs to whichever team's key it arrived on.
+
 ## Upgrading to roles
 
 Before this release every authenticated caller could create and delete users,