Sports Lens for Canon M50 Mk II

I have a Canon M50 Mk II.  I do some sports photography at my school which means night and indoor games.  Our facilities are well lit, and I've gotten adequate shots with the EF-M 55-200 f / 4.5 to 6.3.

Since I can take EF lenses with an adapter, I'm looking at the...

Canon EF 70-200 f / 2.8,

the Canon EF 70-200 f / 4,

and the Canon EF 80-200 f / 2.8.

So, here are my questions:

Should I sell a kidney to get the low aperture lens, or will the f / 4 be distinctly better than what I'm using?

I believe the 80-200 lens does not come with image stabilization.  How important is that if I'm shooting at 1/500th?

Thanks!