What else do people do during the safety stop?
On my deco stops (what you call a safety stop, except every 10' from half the max depth for a minute each on no-deco dives)... if I'm just doing a 30 second stop 30 second ascent to next, I'll just hang around.
Sometimes we'll call for a 3-2-1 minute stops starting with 30'. On those, I'll try to squeeze something in on the 3 or 2 minute portion. Sometimes an ascending air-share, shooting a bag if there's no line (assuming where in sand and decide to do an ascent from 30' instead of kick back to sand at 5' and ascend there ... else you shoot a bag whenever you decide to ascend if there isn't already an up-line)... valve drill, mask replace, mod-S...
If there's a 3rd person familiar with the excercise, we might opt for a toxing diver rescue or a maskless ascent.
Since I'm always taking a class I'm always refining. It started with Essentials, then to UTD Rec2, then to UTD DM, then next is UTD T1 and shortly after T2 and hopefully followed by UTD overhead protocols onto Wreck 1 by this time next year. All just a few months apart from each other. So I'm always getting ready for something. And yes, 90% of my dives are fun dives where the objective is not practice.
For longer than 1 minute deco stops if discussed in advance, we'll throw something in and if the surge isn't too bad that holding position is an ordeal.