feat(tui): inherit session directory when creating a new session

[kitlangton]

What

In the V2 TUI, /new always created the next session in the directory the TUI was launched from, even when the current session lived in a different project. Now the home route inherits the previous session's location — matching the desktop app's new-tab behavior — and the label under the prompt always shows where the next session will be created.

Before: launch in ~/a, open a session in ~/b, hit /new, submit → session created in ~/a, with no indication anywhere.
After: same steps → home shows ~/b under the prompt and the session is created in ~/b. /cd on home overrides it (and the label updates), and a plain launch keeps using the launch cwd.

This also fixes the open menu / project picker: it already navigated home with route.location, but the next session was still created in the launch cwd.

How

The design principle: the location context is where the next session is created. Home seeds it (launch cwd, inherited session location, or picked project), /cd updates it, session.create reads it. No parallel staging state.

• context/location.tsx — the provider exposes ref (the target location as set) alongside current (the server-synced info), so creation and display can honor a location before its sync completes.
• app.tsx — session.new passes the active session's location when navigating home.
• component/prompt/index.tsx — session.create falls back to currentLocation.ref instead of data.location.default(); /cd before a session exists now only sets the context (its extra move-staging call is gone); the under-prompt location label always renders on home.
• routes/home.tsx — the seeding effect tracks only the route location (and, when absent, the default) and calls location.set inside untrack: location.set reads other signals internally, and tracking them re-asserted the route location after a user /cd, silently changing where the session would be created.
• context/route.tsx — documents HomeRoute.location as the carried-over location.

Flow

sequenceDiagram
    participant S as Session route (~/b)
    participant H as Home route
    participant L as Location context
    participant P as Prompt
    participant API as Server

    S->>H: /new — navigate({ type: "home", location: session.location })
    H->>L: location.set({ directory: "~/b" })
    Note over P: label shows ~/b
    opt user overrides
        P->>L: /cd ~/elsewhere — location.set(...)
        Note over P: label shows ~/elsewhere
    end
    P->>API: session.create({ location: currentLocation.ref })

Loading

Scope

• /move's "new working copy" staging is untouched and still takes precedence at submit when explicitly selected.
• Error-path navigations to home (session not found) intentionally do not carry a location.
• Closing the last session tab lands on home with the launch cwd (deliberate: closing is a "done" gesture, not a "continue" gesture).
• No changes to the desktop app, which already inherits the active tab's directory.

Testing

• bun typecheck and bun test in packages/tui (573 pass).
• End-to-end against a hermetic serve instance with termctrl, verified via the server API: launched the TUI in project A with a session in project B; /new showed B on home and created the next session in B; /cd after /new updated the label and created in A instead; plain launch kept the cwd.

Demo

Real end-to-end run (hermetic server, real TUI): session in newtab-b, /new inherits it and the label shows it, new session created there, then /new + /cd overrides back to newtab-a.

newtab-demo2.mp4