24M and 15/16” aerators aren’t fitting

When we purchased our home, the bathtub’s faucet in the master bath no longer had the male aerator attached. I measured the diameter of the opening and found it was about an inch. So I assumed the 15/16” adapter would work. It seemed like it would fit, but it wouldn’t stay. So I tried a 24M aerator and that definitely fit and stayed, but falls out at the slightest touch or whenever you start the water. My tub has no markings of the actual manufacturer, so I’m grasping at straws at this point.

Could it be a 28M? If so, where would I find that type of part... I’m struggling to find one online. Or could it be that the 24M should work but maybe the threading isn’t matching up with the female component? If so, how would I solve for that?

Any help would be appreciated.