docs: headed mode + sidebar agent documentation (v0.12.0)

- README: sidebar agent section, personal automation example (school parent
  portal), two auth paths (manual login + cookie import), DevTools MCP mention
- BROWSER.md: sidebar agent section with usage, timeout, session isolation,
  authentication, and random delay documentation
- connect-chrome template: add sidebar chat onboarding step
- CHANGELOG: v0.12.0 entry covering headed mode, sidebar agent, extension
- VERSION: bump to 0.12.0.0
- TODOS: Chrome DevTools MCP integration as P0

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

connect-chrome/SKILL.md.tmpl

@@ -104,13 +104,27 @@ Tell the user: "Check the Side Panel — you should see the `goto` and `snapshot
 commands appear in the activity feed. Every command Claude runs will show up here
 in real time."
 
-## Step 5: What's next
+## Step 5: Sidebar chat
+
+After the activity feed demo, tell the user about the sidebar chat:
+
+> The Side Panel also has a **chat tab**. Try typing a message like "take a
+> snapshot and describe this page." A child Claude instance will execute your
+> request in the browser — you'll see the commands appear in the activity feed.
+>
+> The sidebar agent can navigate pages, click buttons, fill forms, and read
+> content. Each task gets up to 5 minutes. It runs in an isolated session, so
+> it won't interfere with this Claude Code window.
+
+## Step 6: What's next
 
 Tell the user:
 
 > You're all set! Chrome is under Claude's control with the Side Panel showing
-> live activity. Here's what you can do:
+> live activity and a chat sidebar for direct commands. Here's what you can do:
 >
+> - **Chat in the sidebar** — type natural language instructions and Claude
+>   executes them in the browser
 > - **Run any browse command** — `$B goto`, `$B click`, `$B snapshot` — and
 >   watch it happen in Chrome + the Side Panel
 > - **Use /qa or /design-review** — they'll run in the visible Chrome window