Why do my safari icons look like this? Some look normal but most of them look like this. On my new iPhone 13 Pro Max.

That happens when a new device is just set up it took mine a day or two for them to look normal.
Update:
It’s been over three days since I set up the new phone and my Safari icons are still not right! Am I stuck with them this way or is there something that can be done to make them change?
Try visiting them. It may be that will refresh your browser cache for the site.