I'm trying to get subdivision to work only on the inner circle. So I applied a crease and sharp edge on the 4 sides of the square but it seems to get ignored. I got this idea from this thread https://blender.stackexchange.com/a/128571/142292 and I already set the crease to 1.0 but it doesn't work. Also Keep sharp edges when using subdivision surface and Forcing a flat edge when using the subdivision surface modifier do not work for me.
It would work with the edge crease on the obliques, but you need to create an additional edge loop:
Edge Crease indicates where you don't want the roudness to happen, as if you used support edges. If you added an edge loop along the outer edges, it would not sharp these outer edges:
Whereas if you bevelled the obliques it would sharp these outer edges: