feat(web): send timezone on login + bootstrap + weekly

Web client posts Intl.DateTimeFormat().resolvedOptions().timeZone to
PUT /api/me/timezone after every successful login, register, and
bootstrap when the locally-stored tz_last_sent_at is >7 days old.
Cadence tracked in localStorage keeps the server stateless on the
"is this stale?" check.

Failures swallowed: the server's UTC default + last-known value keep
the scheduler functioning until the next successful attempt. SSR-
safe via the typeof window guard.

For #392 Half B. Companion Flutter change in next commit.

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

web/src/lib/api/me.ts

@@ -53,3 +53,12 @@ export async function getAPIToken(): Promise<APITokenResponse> {
 export async function regenerateAPIToken(): Promise<APITokenResponse> {
   return api.post<APITokenResponse>('/api/me/api-token', {});
 }
+
+// Submits the browser's current IANA timezone for the authenticated
+// user. Called from the auth store on login + bootstrap + once weekly
+// (cadence tracked client-side in localStorage). Failures are
+// non-fatal — the server's UTC fallback keeps the scheduler working
+// until the next attempt.
+export async function putMyTimezone(timezone: string): Promise<void> {
+  await api.put<void>('/api/me/timezone', { timezone });
+}