ci(web-e2e): prebuild server so Playwright webServer stops timing out

The web-e2e job has been failing on every run with:

    Error: Timed out waiting 120000ms from config.webServer.

Playwright's `webServer` runs `cargo run -p solitaire_server --quiet` and
waits 120s for /health. The workflow cached only npm — no Rust cache — so each
run cold-compiled the entire server graph (axum/sqlx/reqwest/aws-lc-sys) inside
that 120s window and never came up. The browser tests never executed; the
failure was infra, not a web regression.

Fix the harness so the tests actually run:
- add `Swatinem/rust-cache@v2` to warm the cargo cache across runs
- add a `Prebuild server` step (`SQLX_OFFLINE=true cargo build -p
  solitaire_server`) before Playwright, so `webServer`'s `cargo run` reuses the
  compiled binary and starts in seconds (.sqlx offline cache is committed)
- raise `webServer.timeout` 120s -> 300s as a safety margin for a cold cargo
  cache (e.g. first run after a deps bump)

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

solitaire_server/e2e/playwright.config.js

@@ -35,7 +35,11 @@ module.exports = defineConfig({
             `cargo run -p solitaire_server --quiet`,
         cwd: repoRoot,
         url: `http://127.0.0.1:${serverPort}/health`,
-        timeout: 120_000,
+        // CI prebuilds the server (see web-e2e.yml) so `cargo run` reuses the
+        // compiled binary and starts in seconds. The generous timeout is a
+        // safety margin for a cold cargo cache (e.g. first run after a deps
+        // bump) where `cargo run` may still recompile.
+        timeout: 300_000,
         reuseExistingServer: !process.env.CI,
     },
 });