Serve the backend under a base path: one URL per environment, the backend under /api

The test deployment keeps one base URL per environment, as the sibling
ActivityPods apps do, so a pull-request preview lives on a single host: the
app at the root, the backend under /api on the same host, its /.well-known
routes at the origin root, the proxy passing paths through unchanged.

SemApps already works that way — it mounts every route it adds under the base
URL's path and keeps /.well-known at the root — but Festipod's own pieces were
written for a backend at the root of its own origin: its routes (/app,
/as/actor/app, /catalog) were mounted at fixed paths, the public-surface
allow-list matched fixed paths (so under /api every request would have been
refused), and the Solid-OIDC client_id joined the raw request path to the base
URL, which would have repeated the base path (/api/api/...).

base-path.js derives the base path from SEMAPPS_HOME_URL; the routes are
mounted under it; the allow-list matches paths relative to it, the two
/.well-known endpoints against the full path; the client_id is the requested
URI rebuilt from the base URL as written, equal byte for byte to the actor
URI and to what the front end derives. At the root every gate decision is
identical to before (compared over ~8M method/path cases). The rights matrix
probes /.well-known at the backend's origin root.

Verified: bun test (424 pass); the full gate at the root; and the built images
behind a local proxy routing /api and /.well-known unstripped with the Host
header kept — login flow, rights matrix 98/98, revocation.

scripts/e2e-rights-matrix.ts

@@ -774,7 +774,10 @@ async function tracked(): Promise<void> {
  */
 async function publicSurface(): Promise<void> {
   const G = 'backend public surface (anonymous GET, status codes only)';
-  const status = async (path: string): Promise<number> => (await http('GET', `${BACKEND}${path}`)).status;
+  // A path is under the backend's base URL; a full URL is taken as is.
+  const status = async (target: string): Promise<number> => (await http('GET', /^https?:\/\//.test(target) ? target : `${BACKEND}${target}`)).status;
+  // The /.well-known endpoints sit at the backend ORIGIN's root whatever its base path (`/api` on Coolify, backend/services/base-path.js).
+  const atOriginRoot = (path: string): string => `${new URL(BACKEND).origin}${path}`;
   const pathOf = (uri: string | undefined, what: string): string => {
     const u = need(uri, what);
     if (!u.startsWith(`${BACKEND}/`)) throw new Error(`${what} is not on the backend (${u})`);
@@ -794,12 +797,12 @@ async function publicSurface(): Promise<void> {
         pathOf(linkId(actor?.['publicKey']), 'the app actor\'s public key (GET /as/actor/app)'),
         groupPath,
         pathOf(linkId(arrayOf(group?.['interop:hasAccessNeed'])[0]), 'an access need (the access-need group)'),
-        '/.well-known/context.jsonld', '/.well-known/nodeinfo', '/nodeinfo/2.1',
+        atOriginRoot('/.well-known/context.jsonld'), atOriginRoot('/.well-known/nodeinfo'), '/nodeinfo/2.1',
       ];
       const codes = await Promise.all(paths.map(status));
       return { ok: codes.every(c => c === 200), actual: paths.map((p, i) => `${shown(p)} ${codes[i]}`).join(', ') };
     });
-  const webfinger = `/.well-known/webfinger?resource=${encodeURIComponent(`acct:app@${new URL(BACKEND).host}`)}`;
+  const webfinger = atOriginRoot(`/.well-known/webfinger?resource=${encodeURIComponent(`acct:app@${new URL(BACKEND).host}`)}`);
   const refusedPaths = [
     '/', '/key', '/sparql', '/sparql?query=ASK%7B%7D', '/settings', '/proxy', '/_acl', '/.webhooks',
     '/interop/application-registration', '/interop/access-grant', '/interop/data-grant',