Hey there, DaCatmaster.
We understand you're wondering where the screenshots will be when taken from an Apple Watch and, also asking if there is a way for screenshots or photos to save on the Apple Watch directly versus using the iPhone the Apple Watch was set up with.
If you take a screenshot of your Apple Watch, you should be able to find that screenshot in the Photos app on the paired iPhone under Albums, then Screenshots. If you'd like, you can read more about that here: How to take a screenshot on Apple Watch
As for photos syncing to the Apple Watch, that would be from the paired iPhone. You can read more about that here: Choose a photo album and manage storage on Apple Watch
If the Apple Watch SE was set up for a family member and doesn't have a paired iPhone, you can still select a photo album from the iPhone that manages the Apple Watch and how many photos the Apple Watch can display: Set up a family member's Apple Watch
We hope that information helps. Take care.