fix(base-path): keep the crash beacon under the mount, strip CODEMAN_BASE_URL in tests, add the wiring test

The merge-time items from the #381 review. navigator.sendBeacon is not fetch,
so the base-aware wrapper never saw the two crash-diag beacons and a sub-path
install posted them to the origin root every two seconds. The test suite now
strips CODEMAN_BASE_URL like CODEMAN_GESTURE, since the constructor reads it
as a fallback and an operator who exports it would see the root-install
byte-identity assertions fail. test/base-path-server.test.ts boots a real
WebServer under /codeman and checks the ingress strip, the base injection,
the rebased redirects, the 404 envelope and a prefixed WebSocket upgrade.

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

test/test-env-isolation.test.ts

@@ -30,6 +30,7 @@ const STRIPPED_ENV_VARS: Array<[name: string, why: string]> = [
   ['CODEMAN_PASSWORD', 'auth from a running instance would make protected routes behave differently'],
   ['CODEMAN_USERNAME', 'same, and it changes which owner scoping resolves to'],
   ['CODEMAN_GESTURE', 'flips renderIndexHtml output and breaks byte-identity assertions'],
+  ['CODEMAN_BASE_URL', 'mounts the server under a sub-path and breaks the root-install byte-identity assertions'],
   ['CODEMAN_INSTANCE', 'moves the data dir to ~/.codeman-<name> and the tmux socket to codeman-<name>'],
   ['CODEMAN_DATA_DIR', 'ABSOLUTE override: bypasses the temp HOME and points the suite at a real data dir'],
   ['CODEMAN_TMUX_SOCKET', 'renames the socket resolveTmuxSocketName() returns'],