feat: add Export GIF link to finished game pages

[byte-the-bot]

DO NOT MERGE UNTIL

Production BASE_URL is set on Cloud Run. It is currently unset, so
AppConfig::from_env() falls back to http://localhost:3000 and this link would
render as a dead engine_url=http://localhost:3000/api.

This is a pre-existing prod bug, not one introduced here. The board replay iframe
already on every prod game page renders the same dead origin today, as does the Share
input. Evidence (2026-08-15), curl -s https://arena.battlesnake.com/games/25d659a4-75b3-4c7a-8712-77d8c69aee15:

engine=http://localhost:3000/api
value="http://localhost:3000/games/25d659a4-..."

So the Export GIF link would be exactly as broken as the replay viewer sitting directly
above it — no worse. Merging this before BASE_URL is fixed is a defensible call; the
draft status is a safety default, not a veto. Corey decides.

Fix (needs write access to the Cloud Run service — Byte's gcloud identity is
byte-readonly@battlesnake-production.iam.gserviceaccount.com, read-only):

gcloud run services update <service> --region <region> \
  --update-env-vars BASE_URL=https://arena.battlesnake.com

Use --update-env-vars, NOT --set-env-vars: the latter wipes every other variable
on the service (DATABASE_URL, GCP_LOGGING, ENGINE_DATABASE_URL, the Eyes IDs, ...).
This creates a new revision, i.e. a rolling restart of production arena.

After it lands: reload a finished game page and confirm the source now shows
https://arena.battlesnake.com in both the board engine= URL and the Export GIF
href, then mark this PR ready for review.

Tracked follow-up for the deploy job: BS-583fb9517dc14ef9 (make ci.yml pass
--update-env-vars BASE_URL=... so this stops being untracked manual state).

Exporter gate

Ran 2026-08-15 against game 00c0ed77-51f4-4663-81b4-6d6f2e0df1cd: status=200 content_type=image/gif bytes=233989 time=4.90s, x-cache-hit: miss (fresh render,
not a CDN replay), magic bytes GIF89a. (A first attempt against game
3bcc20ac-86bc-4f5d-bca5-ac79036ca2f9 came back x-cache-hit: hit with age: 31883
— inconclusive per protocol, retried with a different game.)

Whoever flips this PR out of draft must rerun the full gate — fresh game discovery
from a snake profile, header capture, x-cache-hit: miss required — as the last action
before merging, and paste the result as a PR comment. Reusing the game ID above is not
acceptable: within 7 days it is a guaranteed cache hit.

What this does

Adds an Export GIF link to the game page's action row (GET /games/{id}), rendered
only when the game's status is finished, linking to
https://exporter.battlesnake.com/games/{id}/gif?engine_url={BASE_URL}/api. The
exporter fetches frame history from the engine-compatible {BASE_URL}/api/games/{id}/frames
endpoint shipped in #127, so the /api suffix in the URL is load-bearing. Plain outbound
anchor (target="_blank" rel="noopener", bare .btn like its siblings) — no proxying,
no request-time health checks, no JavaScript; exporter downtime is the exporter's error
page. Renders for anonymous and authenticated viewers alike (not nested under the
auth branch). og:image/meta tags are out of scope by spec.

Deliberate limitations (decisions, not misses)

• Archived/legacy games are finished with no local frames, so they get a link that
  renders nothing. Accepted: they have no game_battlesnakes rows, so every user-facing
  listing excludes them — reachable only by typing a UUID; the page already shows its
  degenerate "0 snakes" state, and Game/get_game_by_id don't carry archived_at.
  If arena ever surfaces archived games in a listing, gate the link on
  archived_at IS NULL at that time.
• Failed games never get the link, even though they're terminal: gated strictly on
  == GameStatus::Finished, not an "is the game over?" heuristic.
• Exporter output is CDN-cached per game path for 7 days; re-exports return identical
  bytes. Harmless — finished games are immutable.

Tests

• Unit: export_gif_url exact-string test (full URL incl. /gif, ?engine_url=,
  trailing /api — a regression can't silently fall back to the exporter's default engine).
• E2E presence: finished page, exact href/target/rel via getByRole + toHaveCount(1).
• E2E absence: table-driven over waiting/running/failed, toHaveCount(0).
• Full Rust suite (612 tests) and full Playwright suite green locally; the one local
  failure is the known Lima-VM-only game-list.spec.ts job-timing flake (fails on
  main too, passes on CI).