[FEATURE] Desktop Browser pane: password manager support (Apple Passwords / 1Password)

Problem
I use the Browser pane so Claude can work in vendor portals for me. There's no way to save or autofill passwords in it, so every time a site logs us out I have to copy the password out of Apple Passwords and paste it in myself. Keep cookies helps, but it doesn't solve the login itself.

Proposed solution
Let the pane use a password manager the same way Claude in Chrome does with 1Password, where I approve the fill and Claude never sees the password. Apple Passwords support would be great too, since that's what most Mac users already have.

Related: #87853 (auto-closed as inactive, but still an issue) and #100140 (Bitwarden request).