feat(web): move branch selector into the toolbar breadcrumb

[guitavano]

Summary

Moves the GitHub branch selector out of the chat composer and into the shell breadcrumb, so the toolbar reads deco › org › agent › branch.

• New BranchCrumb in shell-breadcrumb.tsx, rendered after the agent crumb. Shows only inside a thread whose agent is a sandbox agent (GitHub repo with an attached connection). Non-sandbox agents (e.g. Decopilot) get no branch crumb.
• The breadcrumb lives above ChatContextProvider, so it can't read the chat task context — BranchCrumb resolves the active thread's branch + lock state from the ThreadManager store instead (harness_id != null ⇒ runtime pinned ⇒ branch locked, matching ChatTaskContextValue.isThreadLocked).
• Reuses the existing BranchPill with placement="header", restyled ghost (no border/bg, hover:bg-accent/60) to match the agent crumb.
• Drops the ChatModeRow wrapper: the chat composer (input.tsx) and agent home (agent-home.tsx) now render ModePicker directly. BranchPill tests moved to their own branch-pill.test.tsx.

Testing

• bun run check ✅
• bun run lint ✅ (0 errors)
• bun test apps/mesh/src/web/components/chat/ ✅ (366 pass)

Notes / follow-up

• Lock timing: in the chat the branch locked as soon as messages existed; in the breadcrumb it locks when harness_id is pinned (first send). There's a brief window where the branch stays editable until the runtime is actually pinned — which is arguably the more correct semantic.
• Worth a visual check on mobile, where the breadcrumb row is tight; the chip truncates at max-w-[200px].

🤖 Generated with Claude Code

---

Summary by cubic

Moved the GitHub branch selector from the chat composer into the toolbar breadcrumb so it reads “org › agent › branch”. It shows only in sandbox-agent threads and avoids rendering for off-list/archived threads.

• New Features

  • Added BranchCrumb in shell-breadcrumb.tsx that renders BranchPill. Lock state comes from the ThreadManager store (harness_id != null), and updates use useThreadActions.setBranch.
  • BranchCrumb gates on the active thread being present in the panel store; off-list/archived threads render nothing to avoid an unlocked, branch-less picker and phantom “New chat” rows.

• Refactors

  • Removed placement from BranchPill/BranchPicker; always render a ghost, header-styled chip with a visible label. Simplified styles and removed responsive label collapse.
  • ChatModeRow now only renders the RuntimeSwitcher or the locked-runtime chip; removed branch pill composition and ChatModeRowPure. Callers in input.tsx and agent-home.tsx updated.

^{Written for commit 8416e38. Summary will update on new commits.}