src/core/client-apps.ts reads, for each of a client's apps, the title of the work running now or of the last change landed in 7 days #4007

First half of #3344. It adds data only and changes no page.

Done:

• [ ] A new clientDoings(db, appIds, now) in src/core/client-apps.ts makes one bounded SQL read (one query for all the apps, LIMIT by app count) and returns plain data per app: { kind: "working", title }, { kind: "landed", title, at } or nothing.
• [ ] A running run linked to an issue wins over a landed change. A change landed more than 7 days ago is ignored. A running run with no issue yields nothing.
• [ ] Tests in test/client-home.test.ts (or a new test/client-apps.test.ts) cover working, landed inside the week, landed outside it, working beating landed, and a quiet app. They fail without the change.
• [ ] bun x tsc --noEmit is clean. Nothing calls the new function yet, so the preview deploys exactly as main does.

Files: src/core/client-apps.ts and one test file. Risk: the run and issue columns. Reuse the queries client-apps.ts already makes rather than new joins on unindexed columns.