I am having the same problem. It actually Samuels like electrical burning smell not really a plastic burning smell.
Clearly there is something going on here as I have owned every Note version that was released even the dreaded Note 7. I hope there is not going to turn out there is a problem with the s23 Ultra that requires a recall.
It is wrong that this is getting dismissed by support. Not really a very convincing response to say it's gassing off etc. It never happened before.
I have been involved with electronic repair for many, many years and although I'm no specialist in the Samsung pen, to me it smells like a battery issue within the open.
It is worth noting though the open doors still function ok.