Project and thread switchers in the chat breadcrumb

[mollymillions-code]

Problem

The chat header breadcrumb (Project / Thread title) shows where you are, but you can't move from it. Clicking the project starts a new thread, and clicking the title opens thread actions. To switch to another project or another thread in the same project, you go back to the sidebar and scan for it. That's slow with many projects, or with long settled lists where older threads aren't even loaded. The mobile app makes switching feel lighter, and I'd like the same on desktop and web.

Proposal

Turn both crumbs into searchable dropdowns:

• Project crumb: every project in sidebar order, with search. Picking one opens that project's most recent thread, or a new thread when it has none. "New thread in " stays as the first item, so the current click behavior is still one click away.
• Thread crumb: the project's threads, pinned first, then the sidebar's thread sort, with search. Older settled threads load on demand while the menu is open, through the same shelf paging the sidebar uses. "New thread" is the first item. "Thread actions" is the last item, and right-click still opens thread actions. Double-click still renames.

No contract or server changes. The list hooks live inside the popup, so the header subscribes to nothing extra while the menus are closed.

Before	After: project	After: thread

Open questions for maintainers

• Is moving thread actions off the plain click acceptable (right-click plus a menu item), or should the title keep opening actions, with the switcher on the chevron only?
• Should picking a project land on its latest thread (proposed) or open a new thread?

A working implementation is on mollymillions-code/t3code@feat/breadcrumb-switchers, and I've opened a PR so it can be reviewed against this. I'm happy to reshape it, or to close it, depending on the direction you approve.

Written with Claude Code (Claude Opus 5.5 as architect) and GPT Sol 6.1 (Codex) for UI and tests.