yore Does Play Services communicate with it in any way?
They're both proprietary apps, so there's no easy way to figure this out, and even if we did then functionality could change after an update at any time. I personally don't suspect Markup does anything that shady because it's a very small and simple app by all accounts. Also, on Pixel phones, Google Photos and Google Play Services usually have access to everything anyway. Adding that kind of functionality to a small app would be redundant, so I really doubt the app is anything more than what it appears to be. It's also worth noting that the app doesn't request any permissions, including the Network permission.
The functionality of Markup is all speculation on my part, of course. If you don't want to make decisions based on speculation then, honestly, you might consider not using the app.
The markup app would only be able to access files it's sent (not sure how long the app can access the file afterwards) and files it creates. It wouldn't have access to other files.