Pick the browser profile a chat works in (GODM-27)

[danielehrhardt]

What does this change?

Pick the browser profile a chat works in, right from the composer (GODM-27).

• Composer chip (new chat + existing chat):
  • A quiet "Browser" button while the chat uses the default profile.
  • A pill with the profile's name once one is picked for the chat. It is dashed when the profile comes from the agent's pin or the workspace default, and shows a live dot while that browser runs.
  • The picker lists every profile with its scope, cookie count and running state. "New profile" creates one and selects it right away; "Manage" jumps to the Browser page.
  • The chip is hidden when the agent has no browser, and when the chat works in a VM (its browser then runs in the guest).
• Resolution: the chat's profile, else the agent's pinned one, else the workspace default, else the global default. Stored in conversations.browser_profile_id (migration 11).
• Runs: the browser lock, the browser-use MCP server, vault fills and missing-login detection all use the same profile, resolved once when the run starts. A chat waiting for a busy browser starts as soon as it's switched to a free profile.
• Delegation: work for an agent without a pinned profile keeps the profile picked for the caller's chat, when that profile is global or in the target agent's workspace.
• Live view: the side panel follows the chat's profile and its footer says "Picked for this chat". If you switch mid-run, the panel keeps showing the browser the agent is still driving; the new profile applies from your next message.
• Deleting a profile sends its chats back to their default.
• The composer's context tray now wraps instead of squashing chips on narrow windows.

How was it tested?

• pnpm typecheck: clean.
• bun test in packages/core: 650 pass, 0 fail. New tests cover:
  • a chat running in its own profile next to a busy default one
  • a waiting chat switched to a free profile starts
  • validation, and clearing on profile delete
  • delegation inherits the profile within reach, and not across workspaces
• macOS, dashboard via vite + core on an isolated GODMODE_HOME:
  • picking and resetting a profile on the home page and in a chat
  • the dashed state for an agent-pinned profile
  • "New profile" from the picker
  • the side panel footer
  • the tray at 420–1440px wide

Screenshots are attached to GODM-27.

Checklist

• pnpm typecheck and pnpm test pass
• cargo clippy / cargo test pass (if apps/desktop/src-tauri changed) — not changed
• API changes are reflected in packages/shared and apps/desktop/src/lib/api.ts
• No secrets, tokens or personal data in code, fixtures, logs or screenshots
• Docs updated where behaviour changed (docs/ARCHITECTURE.md)