Agent and Inbox: full pages, denser dock

Large Agent and Inbox surfaces now live on their own routes, and the floating dock stays for lightweight chats.

Agent

Full-page Agent chats: / stays a draft composer; the first send creates a session and continues on /agent/[sessionId]
Site header chat switcher (search, new chat, history) on Agent surfaces; Move to dock opens the floating AI panel
Attaching a file on Home no longer navigates away mid-upload — the draft session stays mounted until you send

Full-page Inbox for startups: /inbox and /inbox/[id], with a sidebar entry under Agent
Dock Expand opens the page route instead of an expanded overlay; the floating dock remains for lightweight chats
Conversation list grouped by Task / Team / Archived sections (no category rail or dropdown)
Compact list rows: smaller avatars, icon-only status, no time or message preview; pen-only New
Floating Inbox shows list + chat side by side (~30/70) in a narrower panel; the header shows the selected task or people
Mobile full-page Inbox uses list ↔ chat instead of a cramped two-column layout

Click outside closes the floating Agent or Inbox panel (the bottom bar and popovers stay interactive)
A leftover expanded dock state from older sessions is treated as floating on load, so the first tab click no longer unexpectedly minimizes