Fast test/apps-busy.test.ts: chop and rewrite under the budget (1 s a test, 10 s a file) #1252

Part of #1242. test/apps-busy.test.ts took 26.4s alone in scripts/test-times.json (last recording), so it sits in SLOW in scripts/gate.ts with this issue beside it.

Chop and rewrite, not trim (the owner, on #1242):

• Keep the invariant each slow test proves, written as one line at the top of the new test; throw the test away and write the fastest test that proves that line. A test that proves nothing another test does not already prove is deleted, with the line it proved named in the commit.
• One forge and one server per file, created in beforeAll; no Bun.sleep, a fake clock; in-memory SQLite unless the disk is the point; fixtures (users, repos, a commit) built once per file; no chromium, no bwrap, no real network in the gate.
• Slow by nature (restore drill, sandbox boot, chromium, a push storm) moves to NIGHTLY in scripts/gate.ts, with its reason.

Done: the gate's scripts/test-times.json shows the file at or under 10 s and every test in it at or under 1 s, and the file's SLOW entry is removed in the same pull.

Replaced by #10213: still over the 10 s budget when measured on 2026-11-09; re-planned under P0 now that #1163 is gone.