Add self-service sign-up and invite links

First half of #7. Until now the only way to get an account was for
somebody who already had one to create it, and the login page told people
to "ask an admin" -- workable for one operator, impossible for a team.

Two modes, chosen by an administrator in the settings table: invite_only,
which is the default, and open. A third domain-restricted mode was
considered and dropped, because with no email in this server there is
nothing to verify an address against and it would only check the domain
of a string somebody typed.

The default is the closed door. An install that gets a public hostname
before anybody has thought about sign-up should not be collecting
accounts from the internet, and the failure mode of a typo in the setting
is invite_only rather than open.

An invite is a link, not an email. Adding SMTP to send one message would
be a subsystem to run, secure and monitor; the person inviting sends the
link however they already talk to the person they are inviting. A link
carries the team and the role, because an account in no team sees an
empty queue and can be paged by nobody -- that is not a state to invite
somebody into. Links are single-use by default, expire after seven days,
and can be revoked before that: a link that works forever is a credential
nobody remembers issuing, sitting in a chat log.

The uses counter is incremented inside the sign-up transaction and
guarded by `uses < max_uses`, so two people redeeming the last use at
once cannot both get in.

GET /api/signup reports the mode and whether a link is usable, so the
form can say "this link has expired" before somebody picks a password
rather than after. It gives one answer for expired, revoked, used up and
never existed: telling a stranger which it was tells them something about
links they do not hold.

Sign-up signs you in. The alternative is a form that says "now go and log
in", which is the same credential typed twice. login and signup now share
startSession rather than each minting a cookie.

Rate-limited per address on its own limiter, not login's: a burst of
sign-ups must not lock somebody out of logging in.

The settings table grew a second shape for this. It held only durations;
signup_mode is a word from a fixed list, so the admin endpoint now
validates everything before writing anything -- a request that sets two
settings and gets one wrong changes neither.

Still to come in #7: the sign-up and invite-redemption pages, the
first-run checklist, and the in-app integration instructions. The schema
carries onboarding_dismissed_at for the checklist already.

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

internal/api/auth.go

@@ -139,6 +139,34 @@ func hashPassword(pw string) (string, error) {
 	return string(h), err
 }
 
+// startSession mints a session and sets the cookie. Shared by login and
+// sign-up: somebody who has just chosen a password is signed in, rather than
+// being sent to a form to type the same credential again.
+func startSession(w http.ResponseWriter, r *http.Request, db *sql.DB, userID int64, publicURL string) error {
+	raw, tokenHash, err := randomToken()
+	if err != nil {
+		return err
+	}
+	now := time.Now()
+	if _, err := db.ExecContext(r.Context(), `
+		INSERT INTO sessions (token_hash, user_id, created_at, last_seen_at, expires_at, user_agent)
+		VALUES ($1, $2, $3, $4, $5, $6)`,
+		tokenHash, userID, now.Unix(), now.Unix(), now.Add(sessionTTL).Unix(), r.UserAgent()); err != nil {
+		return err
+	}
+
+	http.SetCookie(w, &http.Cookie{
+		Name:     sessionCookie,
+		Value:    raw,
+		Path:     "/",
+		MaxAge:   int(sessionTTL.Seconds()),
+		HttpOnly: true,
+		Secure:   cookieSecure(publicURL, r),
+		SameSite: http.SameSiteLaxMode,
+	})
+	return nil
+}
+
 // handleLogin exchanges a username and password for a session cookie.
 func handleLogin(db *sql.DB, limiter *loginLimiter, publicURL string) http.HandlerFunc {
 	return func(w http.ResponseWriter, r *http.Request) {
@@ -182,29 +210,10 @@ func handleLogin(db *sql.DB, limiter *loginLimiter, publicURL string) http.Handl
 		}
 		limiter.clear(userKey)
 
-		raw, tokenHash, err := randomToken()
-		if err != nil {
+		if err := startSession(w, r, db, userID, publicURL); err != nil {
 			respond(w, http.StatusInternalServerError, errResp("internal error"))
 			return
 		}
-		now := time.Now()
-		if _, err := db.ExecContext(r.Context(), `
-			INSERT INTO sessions (token_hash, user_id, created_at, last_seen_at, expires_at, user_agent)
-			VALUES ($1, $2, $3, $4, $5, $6)`,
-			tokenHash, userID, now.Unix(), now.Unix(), now.Add(sessionTTL).Unix(), r.UserAgent()); err != nil {
-			respond(w, http.StatusInternalServerError, errResp("internal error"))
-			return
-		}
-
-		http.SetCookie(w, &http.Cookie{
-			Name:     sessionCookie,
-			Value:    raw,
-			Path:     "/",
-			MaxAge:   int(sessionTTL.Seconds()),
-			HttpOnly: true,
-			Secure:   cookieSecure(publicURL, r),
-			SameSite: http.SameSiteLaxMode,
-		})
 
 		user, err := fetchUser(r.Context(), db, userID)
 		if err != nil {