[data grid] Toolbar follow-up tasks

[KenanYusuf]

Master issue for follow-up items since merging #14611 #16814

The following items can be converted into sub issues when ready to be picked up:

• Remove direct usage of Material UI Menu component
• showQuickFilter is now true by default—we can remove where this is set explicitly in demos
• Add tests for toolbar and related components
• Component state documentation [DataGrid] New Toolbar component #14611 (comment)
• Anchor filter panel and columns panel to triggers
• Explore having an "overflow menu" for items that do not fit on the toolbar
• Add toolbar-specific background color theme override/css variable
• Row grouping toolbar demo
• Use toolbar on other demos with buttons to interact with grid [DataGrid] Use new toolbar by default #16814 (comment)