You asked
Is the sony fe 70 200mm f 4 macro g oss ii good for sports?
Yes, for sideline sport it's a sensible choice. The wildlife and sport guide puts 70-200mm at the start of the useful range for sport from the sideline on full frame. It's stabilised and autofocuses, which helps when things move.
Its f/4 maximum aperture is the limit. In dim indoor gyms you'll need a higher ISO than you'd want, so it works best outdoors. If you shoot on an APS-C body like the Sony a6700, it frames like about 105-300mm on full frame, which gives you more reach for the price of less background blur.
For a more compact alternative, the Sony FE 70-200mm f/4 G OSS is the same focal range without the macro focusing. For birds, you'll want longer reach than this; see the reach section.
Written by Claude from this site's pages.