Need Canon upgrade advice. Any ideas?

I am just now getting back into photography after dabbling with it most of my adult life. I am in no way a professional, I am an amateur and do all of my families portraits, kids sports, etc…

Currently I have a 6d mk II with a 135mm f2 L that I pretty much use for everything.i also have the nifty 50 and an 85mm 1.8 but rarely use these.

I have a couple of routes that I can go in upgrading lenses and possibly my camera body.

I am wanting to add the EF 70-200 2.8 IS L II and the EF 24-70 2.8 L II and was going to buy these used since they are much more affordable now.

I realize that if I also choose to upgrade to an R6 mk II that I am going to need an adapter, which is fine with me.

My question is, should I invest in these EF lenses? Will they work okay with an R6 or should I just bite the bullet and go mirror less?

Is there a big difference in quality between the 6D and R6? Is there a big difference in quality between the EF and RF lenses?

I’ll mainly be shooting my kids sports as well as jiu jitsu tournaments and our family portraits. Maybe some video for my business but not a ton.

Hope all of that makes sense. Thanks!