I'm using the native moto text app which has worked fine for my purposes thus far. It wasn't until I tried deleting some extraneous messages from a parking service on the Phone Link that I discovered the non-delete option issue. These delete from the phone without a problem. It's just the WIN11 app on my laptop where the problem occurs.
Actually, I got spoiled with the old native Verizon app years ago that I found quite usable - until they quit supporting it and dropped it altogether. That was one of the reasons among many that I got rid of VZW.