Pinnable browser pane showing a per-session URL

[AThraen]

Summary

Add an embedded browser pane that can be pinned to a fixed screen position (e.g. a grid slot or docked panel), independent of layout/group changes. Instead of hosting a terminal, the pane shows a web page — and the URL it displays follows the active shell session, so switching sessions switches the page to whatever is relevant for that project.

Motivation

When driving multiple agent/dev sessions, each project typically has one "relevant" page — a local dev server, a CI dashboard, a PR, docs. Today that means alt-tabbing to an external browser and hunting for the right tab. A pinned in-app browser that tracks the active session keeps the feedback loop inside CodeShellManager.

Proposed behavior

• A browser pane (WebView2 — already a dependency for xterm.js hosting) that can be opened and pinned at a chosen location, similar in spirit to Pin a shell to a fixed screen position across group changes #50 (pin a shell to a fixed screen position).
• Per-session URL (configurable): each session can have a URL associated with it; when the active session changes, the pinned browser navigates to that session's URL.
• Sessions without a configured URL: keep showing the last page (or a placeholder) — TBD.
• URL should persist with the session in state.json.

Configuration ideas

• Field in the New Session dialog / session right-click menu ("Browser URL").
• Possible synergy with run commands: PostRunUrl already exists on RunCommandItem — a run's URL could optionally open in the pinned pane instead of the external browser.
• Global toggle in Settings to enable/disable the follow-active-session behavior.

Related

• Pin a shell to a fixed screen position across group changes #50 — pinning a pane to a fixed position across group changes (same placement mechanics)
• Add Workspace Overview view: status cards with activity + output preview #57 — Workspace Overview view (another non-terminal pane type in the grid)