“This machine doesn’t need my family photo collection synced to it” is .stignore. It’s a bit confusing because .stignore is more like .git/info/excludes than .gitignore in that it’s not synced between machines[1]. (If you wanted a synced ignores file then you need to #include that file from each machine’s .stignore manually.) And what’s ignored on one machine doesn’t then need to be ignored on the others, which will still sync it between themselves in that case. So no pretty checkboxes, but echo /Photos >>.stignore on the machine in question and you should be good (including to delete the Photos subdirectory on that machine).
Oh! Holy shit, that's SO useful. Thank you for taking the time to explain!