Struggling between RF USM and STM lineup as an amateur

Having shot thousands of pictures of my daughter and other (small) family members you actually could even go the R8 route if you do not intend to use the camera for video.

IBIS is nice to have, but at the beginning newborns are veery static so you have a lot of time to pose your shot or even use a tripod and later on they get so quick that you will probably never go below 1/125s - 1/250s or even faster. In the latter case IBIS does virtually nothing. I used to shoot with the EOS R + 28-70 f/2 and never missed IBIS. For this style of shooting IBIS is purely optional and I don't see any benefit from the IBIS in my R5 or the Nikons I own over the EOS R.

The STM lenses are not spectacular but they will do the job. Even the 85/f2 is fast enough for some running / swinging / jumping playground action.

R5 + RF 85 f/2.0 + 1/1000s, Speeding up on a stone + jumping down, taken from a series, all photos sharp even with the not super fast lens

I actually own the RF 70-200 f/2.8 but I do not think that this is a "must have kids lens". I would either go with a set of primes (16, 24, 35, 40, 50, 85, 105, 135) and maybe mix in one of the truly special lenses (expensive: 50 or 85 1.2, 135 1.8, affordable: 40 + 105 1.4 ART) or use an all purpose lens like the 28-70 f/2 (especially indoors you rarely need something else) or if that is too heavy the 24-70 f/2.8. The adapted Art glas is fantastic and might give you similar results to the much more expensive Canon RF 1.2 glas (e.g. EF 105 1.4 vs RF 85mm 1.2).

Z6 + adapted EF 105 1.4 (Sigma Art), for ultra creamy background full body shots (up to the point of looking "photoshopped")

Body wise the R6 II is certainly a fantastic choice, but still too pricey for what it is (my humble opinion). This body will get interesting if it reaches R6 territory. The R5 was reduced in price recently in europe, maybe you should take a closer look at that, as it is only like 1000€ difference to the R6 II. The R6 is still a very capable camera, if you don't need automatic vehicle or animal detection and do not intend to crop much then this is the current pirce/performance king. The R8 would probably work as well, but of course body wise this is a downgrade (not in terms of IQ or AF though).