Good Sports Lens

I have a Canon M50 MkII.

I do sports photography at my school which means indoor and night games.  Our facilities are pretty well lit, and I've gotten some adequate shots with the EF-M 55-200 f removed link lens.

Of course, I want a better low light lens, and I can take an EF lens with an adapter.  I'm looking at the Canon EF 70-200 lenses which have different max aperatures.  Of course, the higher the f stop, the more affordable the lens.

Should I sell a kidney to get the f removed link , or would an f/4 get better results than what I'm using?

As a follow up question, there is the EF 80-200 f removed link , but it doesn't seem to have image stabilization.  Do I need image stabilization if I can shoot at 1/500th?

Thanks much.