Is it possible to re-generate the sharing links (in case a collaborator has mistakenly published the link)?

Yes, the easiest way to do this is to open a copy of the project via the option on the project listing on your My Projects dashboard. This will generate a new project with a new set of links.

Overleaf Project Open a Copy Screenshot

You can then delete the contents of the original if you wish (depending on how sensitive it is).