[Feature]: Browser Bridge should auto-detect installed Chromium browsers and try Edge when Chrome has no extension

[umnooob]

Feature Description

Problem

OpenCLI currently assumes the Browser Bridge extension is already connected in Chrome/Chromium.

In practice this causes a bad failure mode on machines where:

• Chrome is installed but does not have the OpenCLI extension
• Edge has the OpenCLI extension installed and connected-capable

OpenCLI may fail with extension-not-connected guidance instead of automatically trying other installed Chromium-based browsers.

Expected behavior

When a browser command needs Browser Bridge and no extension is currently connected, OpenCLI should:

1. Detect installed stable Chromium-based browsers on the local machine
2. Try them in a fixed order:
   • Chrome
   • Edge
   • Chromium
3. Stop as soon as any launched browser connects the extension
4. Report which browsers were detected and tried if connection still fails

Why this matters

This is a no-config UX improvement:

• better Edge support
• fewer false-negative "extension not connected" failures
• more accurate recovery behavior for real local setups

Scope

• no CDP fallback
• no new config
• stable channels only
• Chromium-based wording in user-facing guidance

Use Case

support more browsers

Proposed Solution

When the daemon is running but no Browser Bridge extension is connected, OpenCLI:

• detects installed stable browsers in this order:
  • Chrome
  • Edge
  • Chromium
• launches them one by one
• stops as soon as the extension connects
• reports detected and tried browsers in the final error message

It also updates Chrome-only guidance to Chromium-based wording and includes both:

• chrome://extensions
• edge://extensions

Alternatives Considered

No response