Orbit: start screen / recent-analyses picker + in-analysis chat switching

## Ask

There's no easy way to see or switch between the analyses you've worked on. An "analysis" today is just whatever folder happens to be open -- there's no list of recent ones and no start screen to pick from. Reopening the app drops you straight back into the last analysis and its chat.

The reporter keeps each analysis in its own subfolder, and the only way to switch (or start a new one) is **File -> Open Analysis Directory**, which warns it'll clear the current chat and start a new session.

Two rough edges show up around that:

- The warning is misleading -- the chat **isn't** actually cleared. To get the prior chat back you have to run `/chat` for the transcript and `/notebook` for the notebook.
- Orbit only ever opens the **newest** session (by file mtime); there's no UI to reopen an earlier chat within an analysis.

## Proposed direction

A small start screen on launch (VS Code-style): pick a recent analysis, start a new one, or open an existing folder. Within an analysis, a list of past chats you can click to reopen plus a "New chat" button would address the "only newest session opens" gap.

Longer term the reporter suggests grouping analyses under a higher-level **project** (one project spanning several analyses -- ATAC-seq, RNA-seq, etc. -- with shared literature and a running summary), since that's closer to how biologists actually organize work.

The reporter offered to take a stab at a PR for the start screen.

Related: #266 (show current project dir in UI), #21 (session bootstrap: resume/new/review choice), #312 (switched analysis dir not persisted, since fixed).

Start by tracing Orbit's launch behavior, the File → Open Analysis Directory flow, and how it chooses the newest session. Define the scope with the maintainer; done should include a recent-analysis start screen, an explicit new/open flow, and in-analysis controls for reopening past chats and starting a new chat.

Written by the indexing model from the issue text.