From what I've read it does appear that some people have come down with PMR right after having covid shots. Is it the cause for some? It appears that way but I'm not informed enough on that subject to say.
I am concerned that you have dropped your prednisone dose from 25mg to 10 in just a couple weeks. That flies in the face of any recommended reduction rate. Usually a reduction of 10% or less every 3-4 weeks is more common. This isn't a race to get off prednisone, it's reducing at whatever rate that keeps the PMR inflammation and pain under control. Reduce too fast and the pain will let you know! Don't control the pain/inflammation and you'll flare up and start over at a higher dose. Pain is usually an indicator that your dose is too low. I've read that the body introduces a new batch of inflammation every night about 3-4 am. I take my prednisone in the evening which has kept the pain at bay overnight and when I get up. The down side is prednisone is great at messing up sleep patterns at night if taken in the evening but the right dose should then keep the pain controlled. If you do have PMR this is something that is going to take time, carefully controlling the dose to avoid flares and setbacks.

I believe somewhere around 20-30% of those diagnosed are able to get past PMR in around 2 years time. The average was said to be over 5 years and I have talked to some long timers who have had it around 15 years! Doctors often seem to fixate on having one off of Prednisone in 2 years time. While that'd be great it often flies in the face of reality, that a person isn't able to control the pain and get off prednisone that quickly. The cThere's lots of valuable information at this site and healthunlocked.com for PMR sufferers.