For myself and the kids I coach I generally do this in our WU/joint mobility/prevention:
Heel toe raises. On ground if we can't get access to doing them on the beams ( forefoot on beam, heels off ). We 10 feet together, heels together toes out, toes together heels out, 10 on each foot with the other leg in the air.
Sometimes we do heel to toe walks if we have room. We also practice walking on the foot on the outside edge for say 20-40 feet and walking on the inside of the foot. Then we roll our foot from outside to inside and back 15x.
We generally do foot circles both ways 10x.
We hop 40 feet across lines on the floor side to side with the arm circling backwards. This is coordination and warmup for the next drill. Small hops building strength for the next drill which is hopping on one foot for distance. Depending on the height of the gymnast, it's good to do 6 hops across the floor, maybe 7 or 5. We do 1 or 2 passes of these on each foot. Very important to build up that ankle strength for tumbling and vault.
Also bare in mind, that for the last 30 years, I've probably been barefoot 75% of that time or more. I never liked shoes or socks. I wear sandals when I have to outside if it's cold ( cold feet on concrete or asphalt is bad because it sucks away your body heat ) and I've been lucky as a gym coach to generally be bare foot when I'm coaching though I have worked other jobs at the same time requiring shoes or dress shoes.
My ankles are probably very mobile but weaker than I would prefer since doing the one foot bounds for distance usually show they are weak. I've also rolled my ankles tumbling a lot which is common for gymnasts and this has required time off from doing stuff on feet and landings.