No. There are no upgrades specific to 2.6.6.
If there’s a bubble telling you to run something, it’s only because the tool could not run automatically on its own for a previous version.
Usually this is because your site has more than 10k users, but it could also mean the upgrade simply failed for an unknown reason.
The upgrades are non-destructive. You should be able to run them anytime.
The Repair tools are intentionally destructive. They delete a bunch of invisible data and then recalculate it.
It’s wise to backup your data before running them, but you also really shouldn’t have to worry about them.
