Update: when implementing this we can draw on a bug fix which went directly into the wp/6.4 branch.

As suggested by @jsnajdr let's make the "Rename" menu item into a default item within the menu as per BlockLockMenuItem:

We can then remove the filter thus avoiding any perf concerns with the Plugin-based approach.

Alternatively, the rename UI doesn't need to be a plugin. It could be hardcoded directly into the Block Settings Menu, like, for example, BlockLockMenuItem is.

I think what you suggest above is the most pragmatic option for now. This could be actioned in tandem with the follow up in #55194 to make metadata a default global attribute.

Originally posted by @getdave in #55250 (comment)