unlikely
IFF there is a NSA backdoor it likely would be:
- not in paint, but something you can't disable/remove in hardened special purpose windows setups
- not be easily usable by 3rd parties, like some auth accidentally accepting some quite specific other password (e.g. due to some bug reading the expected hash from the wrong place) or similar
lets not forget as much as the NSA might want to spy on you they also want to keep China/Russia out of spying on US companies. A traditional RCE in paint is very counter productive for that.
They (and other governments) can do multiple things at the same time.
One one hand they can actively try to work with companies to get secret back doors put in, sure. But I imagine that's not usually very successful. Lavabit chose to go out of business instead of doing so... I wonder who else is out there that we don't know about.
But we also have evidence that they actively look for, buy, and hoard, unknown (to the vendor) exploits for their own possible later use in case they need it for something.
I'm sure you can imagine that it's much more advantageous to keep collecting all kinds of different ways to get into a system in case one method is not applicable for any number of reasons.
unless they actively work with MS to keep their backdoor fresh, one can reasonably assume a potential backdoor _was_ well-hidden and advanced for the time period when it was introduced. What about after 20 years and LLMs decompiling everything?