How can I fix my distorted options icons?

I'm not sure what you mean by keep your mods, you do need to update to the versions compatible with the game patch of course, but once you have done that you can still play with mods.

Here is the list of broken mods for the latest pack, not all are listed of course, both for the reasons stated in the first post; and for mods to be reported as broken someone needs to report them as such: https://forums.thesims.com/en_US/discussion/990224/broken-updated-mods-cc-may-27-2021-decorator-patch

You can use the 50/50 method



From here:
http://simswiki.info/wiki.php?title=Game_Help:Finding_Problem_Custom_Content#The_50.25_Method