Switch the Web Menu implementation to Base UI

I'm generally interested in seeing whether Compound Web components could be migrated to [Base UI](https://base-ui.com) instead of [Radix UI](https://www.radix-ui-com), as the latter is increasingly unmaintained. A good proof point for this would be our Menu components, as they have some of the most complex interaction with the Radix APIs and have outstanding issues that the move to Base UI could potentially solve for free. It will give us a good idea of the relative quality of the Base UI library.

Start by locating the Compound Web Menu components and comparing their current Radix UI integration with Base UI's Menu APIs. Investigate whether Base UI addresses the outstanding Menu interaction issues mentioned in the issue. Done means the Menu implementation is migrated and the relative quality and unresolved issues are assessed.

Written by the indexing model from the issue text.