I think you are confusing 22WMR and 22WRF. They are not the same. WMR is to WRF what 22long is to 22short.
No I am not confusing the WRF and WMR. There have been several autoloading rifles chambered for the magnum. I know off hand of two. One made by H&R and another made by Heckler and Koch.
There may be WRF’s with jacketed bullets but I have never seen one. All I have ever seen use a lead bullet with a flat nose.
I have never seen a WMR with anything but a jacketed bullet tho the jacket is very thin.