The problem your seeing is that you have too many snapping magnets enabled. It is a bit unfortunate that people don't want to identify what to snap where to snap, which wouldn't have this problem. By rejecting this kind of framework and letting the software just snap what it can is you get much more snapping magnets to manage and even small changes snap you to different places.
Now the default snapping is meant for box layout. Its not doing you any favors. Its not so much that it odes not snap to the center it just prefer to snap to other things too. Ideally youd turn off part of the snapping filters in view menu. But alas photoshop does not give you a fine grained enough options (trying to be simple). But do try some of them like disabling pixel/gridsnap and temporrarily hiding layers you don't want to snap to.
Instead as a alternative try to use arrow keys to nudge in place.
PS: By the way i feel like youd be happier doing this in illustrator because it has a bit more nuanced snapping system (but harder to find options)