Add a Browser tab to the inspector panel (GitHub-aware home page, configurable in Settings ▸ General)

[jiweiyuan]

Summary

Add a Browser as a sixth tab in the right-side inspector panel, so you can view a live web page (dev server, GitHub PR, docs, deploy preview) next to the terminal without leaving termio. The browser's default landing page should be configurable in Settings ▸ General, wired to the existing GitHub integration (e.g. jump straight to the repo / PRs of the current project).

Motivation

When an agent is running a task you constantly bounce out to a browser to:

• check the dev server it just started,
• read the GitHub PR / issue it's working on,
• look at a deploy preview or docs page.

Every one of those is a context switch out of termio. cmux and similar agent-terminals keep a browser pane in-app for exactly this reason. termio already owns the whole inspector surface — adding a browser tab is a natural extension of the panel that already holds git, GitHub/Issues, and Info.

Proposed solution

1. New inspector tab (6th)

• Add a browser case to the inspector-tab enum and a globe/browser SF Symbol to the tab bar (after Info).
• Content view = a WKWebView wrapper (NSViewRepresentable) with a minimal chrome bar: back / forward / reload / URL field.
• Reuse the existing WKWebView pattern from the session-trace HTML dashboard rather than inventing new plumbing.

2. GitHub-aware default URL (Settings ▸ General)

• Add a "Browser" section under General:
  • Home page — free-text URL used when the tab opens with nothing loaded.
  • On open, go to — segmented choice: Home page / Project repo on GitHub / Open PRs.
• When "Project repo on GitHub" / "Open PRs" is selected, resolve the URL from the project's git remote (the same remote resolution the Issues/GitHub pane already uses), so the browser opens on the current project's GitHub page automatically.
• Persist via the existing @AppStorage/UserDefaults settings pattern.

3. Nice-to-haves (follow-ups, not blocking)

• cmd-click a hyperlink in the terminal → open in the browser tab instead of the system browser (termio already intercepts terminal link opens).
• Per-worktree/per-session last-URL memory so switching sessions restores the page you were on.

Scope / non-goals

• Not a full multi-tab browser — one web view per inspector, matching the single-pane pattern of the other inspector tabs.
• No bespoke auth; it relies on the system WebKit cookie store (you're logged into GitHub in Safari/WebKit as usual).

Prior art to reference

• cmux keeps an in-app browser pane alongside the agent for dev-server/PR viewing — worth studying for chrome layout and default-URL behavior.