Tips for shooting dance/drag/burlesque?

I've been asked to take on a primary photographer role for a local troupe I'm friends with, for a show in May. I've previously done videography for them, and since that's fairly hands-off I shot some B-roll stills at the last show, and the results were less than spectacular.

Specifically, my camera seemed to really struggle with autofocus and/or motion blur, since there's a lot of high-speed movement around the stage, so most of my shots came out blurry and soft. Admittedly I'm still an amateur hobbyist so I just had the camera set to Intelligent Auto. Obviously that didn't work out great, so I need some tips on manual settings to use. Thankfully the venue is just a local coffee shop, so there's no real issues with dim light, heavy spotlights, or significant lighting differences between the stage and the room, it's just relatively neutral house lights.

Gear: Sony a6100 with two kit lenses (E PZ 16-50mm f/3.5-5.6 OSS II, E 55-210mm f/4.5-6.3 OSS). I might also have access to a borrowed Sony a7c, also with a kit lens (Sony FE 28-60mm f/4-5.6).