Show team members as a list, with who is on call and who cannot be paged

Team -> Members was a two-column table and an inline add form. It is now
a table in the style of Switches, Sources and Escalation: a status
badge, the member, their role, their next rota day, when they were last
active and when they joined. Adding a member and changing a role moved
into sheets, and removing one asks first.

The badge is the one that matters at 03:00: On call if the rota has them
today, Reachable if they have an ntfy topic, and Can't be paged when a
page to them would go nowhere -- no topic, or a disabled account -- with
the reason under their name. Not being pageable wins over being on call,
since an on-call person nobody can reach is the case worth seeing before
an incident finds it. The rules are the notifier's own. The topic itself
is never in the response, only whether one is set.

Last active is the newer of a member's newest session and API-key use,
and is shown to every member of the team like the rest of the list.
Rota days are UTC dates, and the page formats them as such so a day
cannot show up as the one before.

Removing a member leaves the rota days already assigned to them alone,
which the confirm says, so they are reassigned from the Rota tab rather
than silently dropped.

Demoting the last owner is now refused with 409, as removing them
already was: it was the same outcome by another route, a team with
nobody who can edit it.

API: GET /members gains status, on_call, next_shift, pageable, problem
and last_active_at; additive, no migration, and terdut-tui needs
nothing. POST /members answers 409 for the last-owner demotion.

internal/api/teams.go

@@ -210,8 +210,40 @@ func handleDeleteTeam(db *sql.DB) http.HandlerFunc {
 	}
 }
 
-// handleListTeamMembers names everybody in a team. Visible to any member: you
-// can see who else is on the rota you are on.
+// Member statuses, as the Members page colours them.
+const (
+	memberOnCall     = "oncall"
+	memberReachable  = "reachable"
+	memberUnpageable = "unpageable"
+)
+
+// memberStatus is a team member with what matters about them at 03:00: whether
+// they are on call, whether a page to them would go anywhere, and whether they
+// have been around. The extra fields are output only.
+type memberStatus struct {
+	models.TeamMember
+
+	// Status is unpageable when a page to them would go nowhere — even when
+	// they are on call, since that is the case that matters most — on_call when
+	// the rota has them today, reachable otherwise.
+	Status string `json:"status"`
+
+	OnCall bool `json:"on_call"`
+
+	// NextShift is the first day after today the rota has them (YYYY-MM-DD).
+	NextShift *string `json:"next_shift,omitempty"`
+
+	// Pageable is whether they have an ntfy topic and an enabled account — the
+	// conditions pageLevel and the notifier skip on. Never the topic itself.
+	Pageable bool   `json:"pageable"`
+	Problem  string `json:"problem,omitempty"`
+
+	// LastActiveAt is the last time they used a session or an API key.
+	LastActiveAt *time.Time `json:"last_active_at,omitempty"`
+}
+
+// handleListTeamMembers names everybody in a team, with their status. Visible to
+// any member: you can see who else is on the rota you are on.
 func handleListTeamMembers(db *sql.DB) http.HandlerFunc {
 	return func(w http.ResponseWriter, r *http.Request) {
 		teamID, ok := teamParam(w, r)
@@ -223,26 +255,56 @@ func handleListTeamMembers(db *sql.DB) http.HandlerFunc {
 		}
 
 		rows, err := db.QueryContext(r.Context(), `
-			SELECT m.team_id, m.user_id, u.username, m.role, m.joined_at
+			SELECT m.team_id, m.user_id, u.username, m.role, m.joined_at,
+			       u.ntfy_topic IS NOT NULL AND u.ntfy_topic <> '',
+			       u.disabled_at IS NOT NULL,
+			       GREATEST(
+			         COALESCE((SELECT MAX(last_seen_at) FROM sessions WHERE user_id = u.id), 0),
+			         COALESCE((SELECT MAX(last_used_at) FROM api_keys WHERE user_id = u.id), 0)),
+			       EXISTS (SELECT 1 FROM schedule_entries s
+			                WHERE s.team_id = m.team_id AND s.user_id = u.id AND s.date = $2),
+			       (SELECT MIN(date) FROM schedule_entries s
+			         WHERE s.team_id = m.team_id AND s.user_id = u.id AND s.date > $2)
 			FROM   team_members m
 			JOIN   users u ON u.id = m.user_id
 			WHERE  m.team_id = $1
-			ORDER  BY u.username`, teamID)
+			ORDER  BY u.username`, teamID, todayUTC())
 		if err != nil {
 			respond(w, http.StatusInternalServerError, errResp("internal error"))
 			return
 		}
 		defer rows.Close()
 
-		members := []models.TeamMember{}
+		members := []memberStatus{}
 		for rows.Next() {
-			var m models.TeamMember
-			var joined int64
-			if err := rows.Scan(&m.TeamID, &m.UserID, &m.Username, &m.Role, &joined); err != nil {
+			var m memberStatus
+			var joined, lastActive int64
+			var hasTopic, disabled bool
+			if err := rows.Scan(&m.TeamID, &m.UserID, &m.Username, &m.Role, &joined,
+				&hasTopic, &disabled, &lastActive, &m.OnCall, &m.NextShift); err != nil {
 				respond(w, http.StatusInternalServerError, errResp("internal error"))
 				return
 			}
 			m.JoinedAt = time.Unix(joined, 0).UTC()
+			if lastActive > 0 {
+				t := time.Unix(lastActive, 0).UTC()
+				m.LastActiveAt = &t
+			}
+			switch {
+			case disabled:
+				m.Problem = "account is disabled"
+			case !hasTopic:
+				m.Problem = "has no ntfy topic"
+			}
+			m.Pageable = m.Problem == ""
+			switch {
+			case !m.Pageable:
+				m.Status = memberUnpageable
+			case m.OnCall:
+				m.Status = memberOnCall
+			default:
+				m.Status = memberReachable
+			}
 			members = append(members, m)
 		}
 		if err := rows.Err(); err != nil {
@@ -281,6 +343,20 @@ func handleAddTeamMember(db *sql.DB) http.HandlerFunc {
 			return
 		}
 
+		// Demoting the last owner is removing them by another route: the team
+		// would have nobody who can edit it.
+		if req.Role == models.RoleMember {
+			last, err := isLastTeamOwner(r.Context(), db, teamID, req.UserID)
+			if err != nil {
+				respond(w, http.StatusInternalServerError, errResp("internal error"))
+				return
+			}
+			if last {
+				respond(w, http.StatusConflict, errResp("cannot demote the last owner of a team"))
+				return
+			}
+		}
+
 		_, err := db.ExecContext(r.Context(), `
 			INSERT INTO team_members (team_id, user_id, role)
 			VALUES ($1, $2, $3)