The home timeline ends its first page with "You're caught up" and the time of the oldest post shown, linking to older posts #5980

An X-style feed tells you when you have seen what is new.

Done when:

• [ ] After the last post of the first page, the timeline (src/web/studio/feed.ts) draws one line: You're caught up to <time>, with Older posts linking to the next cursor. With nothing older, the line reads That's everything.
• [ ] It is drawn with §5's existing parts and passes bun scripts/design-lint.ts. Any new class is named in docs/design/areas/feed.md, not docs/DESIGN.md.
• [ ] Tests: a feed with more pages shows the line and the link, and a short feed shows That's everything.