[SDK] Rebuild the session core on PasswordSession behind an AtpAgent compat shim (#11343)

Co-authored-by: Claude Fable 5 <noreply@anthropic.com>

src/storage/schema.ts

@@ -108,4 +108,15 @@ export type Account = {
    * account after a switch, until that account's preferences loaded.
    */
   isBetaUser?: boolean
+
+  /**
+   * The account's subscribed labeler DIDs, cached from preferences so the
+   * `atproto-accept-labelers` header can be configured synchronously at
+   * session start, before preferences load. Eventually consistent: rewritten
+   * on every preferences fetch (see `saveLabelers` in
+   * `#/state/session/moderation`). Until the first fetch lands there is
+   * simply no cache entry and initial requests go out without per-account
+   * labeler headers.
+   */
+  labelers?: string[]
 }