With anonymous access on, land visitors in Chat instead of the login page (#94)

[gangtao]

Follow-up to #95, per feedback: when anonymous access is on, an unauthenticated visitor should be able to try the chat directly, not meet a login page first.

Change (web/src/App.tsx, Login.tsx)

• The mount-time /auth/me check already receives the anonymous identity when the server allows it; it now adopts it as the session instead of only noting it is available. A visitor with no token lands straight in Chat as anonymous, with the "Browsing the public docs" badge and a Sign in button in the sidebar.
• The login page is reached on purpose only: Sign in from the sidebar, or signing out of a real account (both clear the session). It offers Continue without signing in to go back to anonymous chat.
• A failed login stays on the login page with the error — it never falls through to anonymous.
• With anonymous access off, nothing changes: no session → login page, as today.

Checked live (compose stack with TPK_ANONYMOUS_ACCESS=1, fresh bundle)

• / with no session → Chat, nav = [Chat], badge shown, no login form.
• Sign in → login page with the "Continue without signing in" button → back to anonymous chat.
• Reload → lands in Chat again.
• Wrong password → stays on the login page, "invalid credentials".
• Not exercised in the browser: a successful real login and Logout (no valid account password to hand; that code path is unchanged from Anonymous chat over the public corpus, off by default (#94) #95).

Web build + sanitize clean; no backend change, no tests affected.

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