I'm having the same issue with my S20 FE 5G. Mine is my dialing pad though. My lock screen and home have same wallpaper. When I place a call or receive one, my wallpaper is an old one I had A LONG time ago. I can't figure out how to make it match the rest of my phone, or how it's even possible...
This is for Samsung Messages (not Google Messages). Open one of your messages, on the top right click on the 3 dots, you'll see Customize chat room, click on it, it will let you change the background.