The home is the feed, proven end to end: one test walks composer, timeline, crew posts and a share #1802

Replaces #351, whose children #599 and #603 have landed. Done looks like:

• [ ] One end-to-end test (in GATE): signed in, GET / shows the composer, then the timeline; a tell posted through the composer appears as a post; a run or pull appears as the crew member's post with its name; the apps are one link away.
• [ ] Any gap the test finds against #351's intent is fixed in the same pull, or named as a new issue in the pull description.
• [ ] No new feature beyond that.

Files: a new test under test/, src/web/studio/home.ts or src/feed/ only where the test finds a gap.

Start from today's main. Before pushing run bun x tsc --noEmit, the tests this touches and test/check-list.test.ts; name every new test file in GATE in scripts/gate.ts in the same commit. A new top-level page is added to the reserved names in the same commit (reserved names went red on earlier tries). A test that goes red in this pull is fixed in this pull.