Safari crashes when I click the "Manage Website Data" button under Privacy

Safari shouldn't crash at all. Please determine if the same problems occur in "Safe Mode": Start up your Mac in safe mode - Apple Support.

If Safari crashes while loading that page the relevant excerpt for your model Mac is shown below (screenshot):

I didn't think it would, and the reason I didn't even suggest it. Nevertheless, Apple Support is probably going to have you do that anyway, so now you can tell them you did already and it didn't help.

Another idea is to create a new, temporary User Account and determine if you can duplicate the problem while logged in to that Account. It's almost certain the problem will not manifest in that Account, but that determination won't help fix your usual Account. The solution you proposed (erasing the Mac and migrating content from the iMac) is more likely to be successful.

Also likely to be successful, but much more time-consuming, is dragging the entire Safari User Library to the Desktop, followed by methodically dragging components back into it and testing, then repeating until you find the guilty party. I would prefer a more targeted approach, but I would also need to devote the better part of a day to find the exact file or files that need to be fixed or trashed. Perhaps Apple will come up with a faster solution.

Should i try to clear the Manage Website Data option in safe mode and then try and clear it that way?

Yes, do that, and report your results here while remaining in "Safe Mode" (assuming Safari doesn't crash, and you're able to do that).

Then, reboot normally, and repeat.

Yes. Please determine if you can remove the (likely) corrupted data by opening Safari in a Private Window.

The following instructions are excerpted from If Safari doesn't open a page or work as expected on your Mac - Apple Support:

"If that works, use the following steps to remove the website's data, including its caches and cookies. The website can then create new data as needed. If it's a website that you sign in to, make sure that you know your sign-in information before continuing."

They are described under "Test with a private window". Among other potential solutions, that would be the least painful.

If you are not opposed to doing that, it may be the most expedient solution. You might consider migrating its content from the iMac when it asks.

I would like to offer a better solution but have been attempting to duplicate your problem without success... yet.