Maybe give them a call and check if all normal now for camping etc, they can obviously tell you about the bore too.
I found 2 phone entries for Mullorina one from Yellow Pages 08 8675 8341 . . . and one from WIkicamps 08 8648 5300.
I've never done more than travel past their driveway many times, but I believe the camping is reasonable, toilets, bring own drinking water.
A drive to Level Post Bay (if open) is on my list one day, though Lake Eyre South is drying up pretty well.
The track out to Lake Eyre was closed not that long ago. A pretty corrugated track at the best of times. There's not that much else to do out at Muloorina and it's a fair way out and back along the same road.
I stopped in for a look in March while working at one of the pump stations further in on Muloorina. Wasn't anyone camping (was bloody hot, 47°C on the 2nd day). Not too sure what the go is re: covid restrictions
Muloorina Station history - a bit of "slightly off-topic" here, but maybe worth it for a few of you(?) Be patient with the download on this link (I hope it works for you). There are some very fond memories in this for me https://www.bpvideolibrary.com/record/175