[Feature Request] Automatically install Playwright when using BrowserToolkit

[Asher-hss]

Required prerequisites

• [x] I have searched the Issue Tracker and Discussions that this hasn't already been reported. (+1 or comment there if it has.)
• [ ] Consider asking first in a Discussion.

Motivation

Since BrowserToolkit has a hard dependency on Playwright, we should ensure that Playwright is automatically installed to guarantee the tool runs smoothly.

Solution

No response

Alternatives

No response

Additional context

No response