The only way for messages to work on Wifi is to enable RCS chats in Google Messages, open Google message , tap on your avatar top right corner, scroll down to settings, tap on RCS Chats, toggle on RCS chats, toggle on all the features you want.
Interesting, my wife has your phone and she said no problem with her's so far. What about trying this (might write this down) but power off your phone and after 30 seconds hold down the volume up button and the power button at the same time until a menu appears. Use the volume down button send go down to the one that says 'clear system cache' and then hit the power button so that it does it. Then use the volume down button to find one that says either repair or fix apps, you'll see something very similar to that phrase, use the power button again to do it. Hopefully upon reboot it'll be fixed. Let me know and I'll keep thinking
One thing that you can do is 'reset network settings' (settings-general management - reset - reset network settings) but it will cause to pair and sign back into every Wi-Fi network and also pair up any and all Bluetooth items but I honestly do that once a month almost like a maintenance because it gives all your connections a refresh which can clear possible issues and create better connections. If that didn't work I have a few other ideas. One more real easy one is to take out your SIM card and place it back in the slot, sometimes they somehow slightly jostle a bit which causes connection issues. It very well be that you need a new SIM card as well
