Teams appeared with the mouse hole immediately yes. Wasn't universal at first but by the end of 2022 I believe all teams had one to varying extents. I would say its primary purpose has always been to improve diffuser efficiency and probably has some effect on the management of tyre squirt as well.
View this analysis from Kyle Engineers. He first sees it on the AMR22 Launch Spec so that is where he talks about it:
Timestamped to 18mins 47secs if it doesn't work