feat(users): timezone column + PUT /api/me/timezone

Schema + endpoint scaffolding for #392 Half B (per-user timezone
scheduling). Adds two columns to the users table:

  - timezone text NOT NULL DEFAULT 'UTC' (IANA name)
  - timezone_updated_at timestamptz (nullable; populated on each PUT)

PUT /api/me/timezone validates the IANA value via time.LoadLocation
and writes the row. No scheduler integration yet — the scheduler
struct lands in the next commit and the handler-side Refresh call
in the commit after.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

internal/api/api.go

@@ -64,6 +64,7 @@ func Mount(r chi.Router, pool *pgxpool.Pool, logger *slog.Logger, events *playev
 			authed.Get("/me/history", h.handleGetMyHistory)
 			authed.Put("/me/password", h.handleChangePassword)
 			authed.Put("/me/profile", h.handleUpdateMyProfile)
+			authed.Put("/me/timezone", h.handlePutTimezone)
 			authed.Get("/me/api-token", h.handleGetMyAPIToken)
 			authed.Post("/me/api-token", h.handleRegenerateMyAPIToken)