fix(app): discover server projects and sessions across browsers

[BunsDev]

Issue for this PR

Closes #13626

Related: #24035, #51475

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

A fresh browser on a shared server showed no projects, and sessions created
or deleted in another browser never reached the Home list.

Project list: the sidebar came only from this browser's stored project list
(createServerController in runtime/server/runtime.tsx), so a fresh browser
listed nothing even though /api/project had the inventory. The list is now
the browser's opened projects followed by the server's other projects; closing
one stays a local preference. A project registered by another client's first
session arrives as session.created only (the server publishes no
project.updated for it), so that event reloads the inventory once.

Session list: session.deleted from other clients now removes the row, and the
index is refetched when the event stream reconnects, since events sent while
it was down are lost.

No browser-storage migration: discovered projects are derived from the server,
not written to the stored list.

How did you verify your code works?

• New two-context e2e cases in packages/app/e2e/regression/home.spec.ts
  (fail on v2 before the fix): fresh browser discovery, create/rename/delete
  in one browser reaching another, reload / reconnect / cleared storage,
  server and project scoping, failed fetch keeping the sidebar.
• bun run typecheck and lint:changed clean on changed lines.
• Manual check with two Chromium contexts against a real opencode serve
  (isolated data dir): unpatched build lists sessions but no project rows;
  patched build lists projects, including one registered live by the other
  client.

Note: pushed with the local pre-push hook skipped; its bun run typecheck
fails on untouched origin/v2 in this environment too (@opencode/console-app
/ @opencode/stats-app vite.config.ts overload errors). packages/app
typecheck passes.

Screenshots / recordings

Before/after screenshots follow in a comment.

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

[github-actions]

Thanks for your contribution!

This PR doesn't have a linked issue. All PRs must reference an existing issue.

Please:

1. Open an issue describing the bug/feature (if one doesn't exist)
2. Add Fixes #<number> or Closes #<number> to this PR description

See CONTRIBUTING.md for details.

[github-actions]

The following comment was made by an LLM, it may be inaccurate:

[github-actions]

Thanks for updating your PR! It now meets our contributing guidelines. 👍

[BunsDev]

@Hona @Brendonovich (app CODEOWNERS) — could one of you approve the workflow runs on this fork PR when you have a moment? test/check/nix-eval are waiting on first-contributor approval.

Two notes for triage:

• needs:issue is a false positive: the description has Closes #13626, but the standards check only reads closingIssuesReferences, which GitHub leaves empty for PRs targeting v2.
• This overlaps the project-list half of fix(app): show server-known projects in project lists #51475 and adds the session-list side (session.deleted from other clients, refetch on reconnect, and inventory reload on session.created for a project the client hasn't seen, since the server sends no project.updated for it). Happy to rebase onto fix(app): show server-known projects in project lists #51475 if you'd rather land that first.

[BunsDev]

Before/after on a real opencode serve (fresh data dir), browser B opened with empty storage after browser A created sessions in two projects.

Before (v2 @ 34cf183): sessions arrive from /api/session, but the sidebar has no project rows — only "Add project".

After (this PR): the fresh browser lists projA and projB from the server inventory (projB was registered live by browser A while B was open), alongside the same sessions.