I have the 6P and the original stand on my desk at work and have no issues. I did have that same issue with my Pixel 4XL in September/October, in my case it turned out the wireless charging in the phone was going bad. It quickly went from always saying to realign to just charging wireless at all. Though for me it happened pretty quickly. Hopefully that it not the case with yours.
On a side note, I got the new pixel stand for Christmas which I use at the house. Today was the first day I hooked up my original pixel stand at work and used it and I noticed the battery got warm. Nothing worrisome, just noticeable. Just sure if I got used to it before, just noticed it, or its new.