feat: add GitHub Actions CI and support hosting under a subpath

Mirrors the GitLab pipeline — typecheck, tests, feed sanity — and adds a
Pages deploy.

Pages serves from /<repo>/, and the app used absolute asset paths, so that
job would have shipped a site that 404s on everything. Assets now resolve
against a <base href> the build substitutes, the feed URL resolves against
document.baseURI so deep links work too, and the service worker derives its
paths from its own registration scope. Root-hosted builds are unchanged.

Co-Authored-By: Claude Opus 5 (1M context) <[email protected]>

src/client/sw.js

@@ -15,8 +15,12 @@
  */
 
 const CACHE_VERSION = "event-clock-v1";
-const SHELL = ["/", "/index.html", "/styles.css", "/main.js"];
-const FEED = "/data/events.v1.json";
+// Paths are derived from the registration scope, so the same worker is
+// correct at a domain root and under a subpath (GitHub Pages) alike.
+const BASE = new URL("./", self.registration.scope);
+const at = (path) => new URL(path, BASE).toString();
+const SHELL = ["", "index.html", "styles.css", "main.js"].map(at);
+const FEED = new URL("data/events.v1.json", BASE).pathname;
 const FONT_HOSTS = new Set(["fonts.googleapis.com", "fonts.gstatic.com"]);
 
 self.addEventListener("install", (event) => {