It is quite likely that Snipping Tool is also doing this. Every camera also leaves device specific signature because of its inherent silicon sensor defects.

If you want to stay anonymous, don't share images you can't verify at the byte level. Apply filtering to decrease the low bit noise that could hide cryptographic signatures. Don't trust complex container formats.

See e.g. PPM format: https://www.cs.swarthmore.edu/~soni/cs35/f13/Labs/extras/01/...

These days entire scenes can be tweaked by AI to add unimportant but identifying marks, at a level far above signal processing tricks, like moving objects in the scene. Verify from multiple sources.