Serve Firebase's auth handler from our own domain

Google sign-in fails in production: the popup opens, flashes, closes, and the
page shows a generic failure with nothing in the console or the network tab.

The app is served from drb.cusano.net while signInWithPopup opens its handler on
the project's firebaseapp.com origin. Chrome partitions third-party storage, so
the popup cannot read back the state its opener wrote and dies immediately.
Visiting the handler directly says so: "missing initial state ... a
storage-partitioned browser environment". Nothing about authorised domains or
the build was wrong -- the shipped bundle carries the correct apiKey and
authDomain, which is exactly what made this look like a code bug.

Caddy now proxies /__/auth/* on the bare domain to the Firebase Hosting origin,
rewriting Host so Firebase recognises the request. Same-site again, which is
Google's documented fix. The vhost becomes a `route` so the handler matches
before the catch-all proxy to Next.

The upstream host is a jinja default rather than a group_vars entry because
group_vars/all.yml is gitignored; override it there if the project ever moves.

Two manual steps remain, and all three parts are required or nothing changes:
the CI secret FIREBASE_AUTH_DOMAIN must become drb.cusano.net with a frontend
rebuild, and drb.cusano.net must be an authorised domain in the Firebase
console. This template also needs an ansible run -- CI alone will not deploy it.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

infra/ansible/roles/deploy/templates/Caddyfile.j2

@@ -35,7 +35,31 @@ mqtt.{{ domain }} {
 # To move it to app.{{ domain }}, create the A record first, then change this
 # line — the reverse_proxy target stays the same either way.
 {{ domain }} {
+  route {
+    # Firebase Auth's sign-in handler, served from our own origin.
+    #
+    # signInWithPopup opens {{ firebase_auth_handler_host | default('discord-radio-bot-461301.firebaseapp.com') }}/__/auth/handler and
+    # then reads back state the opener wrote. Chrome now partitions third-party
+    # storage, so when that handler is on a different site from the app the
+    # popup cannot see that state: it opens, fails, and closes instantly with no
+    # console or network trace. The handler page says so itself if you visit it
+    # directly ("storage-partitioned browser environment").
+    #
+    # Proxying the handler through this domain makes it same-site, which is
+    # Google's documented fix. Host must be rewritten upstream or Firebase
+    # Hosting will not recognise the request.
+    #
+    # NEXT_PUBLIC_FIREBASE_AUTH_DOMAIN must be set to {{ domain }} in the CI
+    # build secrets to match, and {{ domain }} must be listed in the Firebase
+    # console's authorised domains. Changing only one of the three does nothing.
+    handle /__/auth/* {
+      reverse_proxy https://{{ firebase_auth_handler_host | default('discord-radio-bot-461301.firebaseapp.com') }} {
+        header_up Host {{ firebase_auth_handler_host | default('discord-radio-bot-461301.firebaseapp.com') }}
+      }
+    }
+
     reverse_proxy localhost:3000 {
       header_up X-Forwarded-For {remote_host}
     }
+  }
 }