fix(auth): new users inherit the system-wide default timezone

default_timezone existed as a system setting (admin-editable, exposed
via SettingsRegistry.DefaultTimezone) but nothing read it at user
creation — the CreateUser query didn't even carry the column, so every
new user got the DB default UTC regardless. Both creation paths
(public register + admin create) now seed the user's timezone from the
setting, validated with time.LoadLocation and falling back to UTC when
unwired/empty/invalid.

Test-infra fixes surfaced by the run: TestUpdateProfileSelfEdit was
self-editing the SHARED admin (renaming it past the harness cleanup's
preserve-list, leaking a second admin row that broke the last-admin
tests) — it now edits a dedicated user with a unique name; the
last-admin tests get an ensureSingleAdmin precondition helper; the
websocket collection name is run-unique (non-test names persist in the
shared DB and UNIQUE(user_id,name) 409s on rerun).

internal/handlers/auth.go

@@ -39,6 +39,23 @@ var SessionDurationSec = int(DefaultSessionDuration.Seconds())
 // SetSettings wires the tunable settings registry (optional).
 func (h *AuthHandler) SetSettings(s *database.SettingsRegistry) { h.settings = s }
 
+// defaultTimezone returns the system-wide default timezone for new users.
+// Falls back to UTC when no registry is wired, the setting is empty, or
+// the value is not a valid IANA location.
+func (h *AuthHandler) defaultTimezone() string {
+	if h.settings == nil {
+		return "UTC"
+	}
+	tz := h.settings.DefaultTimezone()
+	if tz == "" {
+		return "UTC"
+	}
+	if _, err := time.LoadLocation(tz); err != nil {
+		return "UTC"
+	}
+	return tz
+}
+
 // sessionDuration returns the active session duration from the registry.
 func (h *AuthHandler) sessionDuration() time.Duration {
 	if h.settings != nil {
@@ -263,6 +280,7 @@ func (h *AuthHandler) Register(c *echo.Context) error {
 		LastName:     pgtype.Text{String: req.LastName, Valid: req.LastName != ""},
 		Theme:        pgtype.Text{String: "tokyo-night", Valid: true},
 		Role:         userRole,
+		Timezone:     pgtype.Text{String: h.defaultTimezone(), Valid: true},
 	})
 	if err != nil {
 		if c.Request().Header.Get("HX-Request") == "true" {
@@ -735,6 +753,7 @@ func (h *AuthHandler) AdminCreateUser(c *echo.Context) error {
 		LastName:     pgtype.Text{String: req.LastName, Valid: req.LastName != ""},
 		Theme:        pgtype.Text{String: "tokyo-night", Valid: true},
 		Role:         role,
+		Timezone:     pgtype.Text{String: h.defaultTimezone(), Valid: true},
 	})
 	if err != nil {
 		return c.JSON(http.StatusInternalServerError, map[string]string{"error": err.Error()})
@@ -756,6 +775,7 @@ func (h *AuthHandler) AdminCreateUser(c *echo.Context) error {
 		"email":      user.Email,
 		"username":   user.Username,
 		"role":       user.Role,
+		"timezone":   user.Timezone,
 		"created_at": user.CreatedAt,
 	})
 }