I would love to know what kind of process you used to determine out of all the camera brands and models, you ended up choosing a Sony mirrorless camera?
I shoot a whole lot of sports. Many of the games are played indoors or at night under the lights. That means that in order for me to stop the action of the athletes, I have to use a shutter speed of 1/500th second or shorter. That also means that I have to set the ISO to 6400
I use a Nikon D500 to give me added reach when using either my 70-200 mm f/2.8, 200 mm f/2.0 or 300 mm f/2.8 lenses and a D800e when using a 24-70 mm f/2.8 along the sidelines to capture the faces of the coaches and players on the bench.
What you should know is that when you use an adapter, you will be losing a whole stop of light and in many cases, all your focusing and lens aperture setting will have to be done manually
Here are two photos shot in low light with "moving subjects"
When shooting subjects which have "stage" lighting, I use a 70-200 mm f/2.8 if I am shooting from the photographers well or 24-70 mm if I have an "all access" media pass and am shooting on stage or backstage before or after the concert or play
Shooting a performance which is on stage is tricky since the lighting director has set up the lighting for each scene and there are pools of light in which the actors or performers spend most of their time. In those situations, you need to get a good light reading and set the camera to manual mode and only take shots when they are in that light