Hello. Looking for professional advice. I am not a professional photographer, therefore I ask dumb questions

. I have an old Canon DS1 and some very large Canon L lenses, including the 3.5 28mm-300mm. I also have the 2.8 24mm-70mm L. ISO on the DS1 is horrible, as the camera is 10 years old before technology got better with ISO.
I plan on downsizing, and upgrading, and have ordered the A7rII. I know I can use adapters and keep the Canon lenses, but my plan is to shrink down the size of my equipment.
I have 5 children also, and they all play sports. Much of my shooting is of them. I would like a zoom lens that I can shoot action photography indoors (ex basketball) and was hoping to get some advice from the people that shoot for a living. I don't see any high end long E-Mount 2.8 tele/zoom lenses. Not sure if the greatly improved ISO on the A7rII will allow an F4 to work well indoors.
Any advice would be appreciated. My goal would be to start with full-frame-mount, smaller and lighter, lenses. Downsizing and reducing weight is a key goal. After that, I can always go the adapter route which would be a second choice.
I would like to replace both my Canon L lenses
I have been told the Sony Vario-Tessar T* FE 24-70mm f/4 ZA OSS Lens would be a great replacement for the Canon 2.8 24mm-70mm L. It is F4, not 2.8, so I am not sure whether that would impact indoor action shooting.
As for the Canon .5 28mm-300mm L, I don't know what to replace it with.
Thanks in advance.