I did some work on structuring my list/logins,

so I copied many passwords briefly and pasted them into additional entries. I did not delete the old entries but changed them because I had put together a few logins, which I now wanted to have listed separately.

Now under the category "Identical passwords" they are now listed although I deleted the passwords after I copied them.

Can I update the list of the password check or are the passwords somehow cached even though I deleted them?

The deleted passwords would be in the "Trash" folder in Enpass. Make sure you empty the "Trash" only after you've saved the passwords somewhere else.