This is probably an unrelated tidbit. But just confirming you have sony V4b blobs flashed (rather than the V3a blobs that Jolla originally instructed to use)? I have far more reliable mobile data on the V4b blobs than I did on the V3a blobs.
Also, my 10V behaves the same as yours if I use the new utility “restart mobile network subsytem”.
Sorry if this offers nothing. Just thought worth checking.
I’ve had the same reoccuring issue on my Xperia 10 III after installing 5.1.0.11. Re-initializing wifi and mobile data subsystems with Sailfish Utilities usually helps.
As a sidenote, I’ve also had major issues with BT after the update as well, but that’s probably due to installing AppSupport Bluetooth beta.