#46343 added the ability to edit block style variations in Global Styles. That was only part of the scope of the initial issue (#44417), but further steps required a few changes to be made to the global styles APIs. Now that #47098 is done, it should be straightforward to add new variations from the global styles UI.
Also, given the addition of per-block custom CSS in #46571, we could consider:

• adding a custom CSS field to block style variations, which would open the door to
• making custom block style variations editable. Even if custom styles are added via a stylesheet instead of theme.json, having a custom CSS field would allow for easy overrides.
• it should also be possible to add custom block style variations via theme.json.