Whenever I try to open the Tau drill's inventory, it disappears instead.
I'm not sure if its affected by quality, but its the second quality level (I don't remember its name, I renamed them; Two green dots)

I'm not having this issue in testing, and it should be okay with any modded quality levels. Is the mod fully up to date (tau has a purple ring and some red panels)?
If yes, what mods are you using that could be affecting it?

It is up to date;
This is the only one that affects the omega drill:
https://mods.factorio.com/mod/quality-miners

From the mod description:
It adds new miner prototypes to the game, so it is inherently incompatible with any other mod that does the same for miners.

Yarp, there's the problem. This will also make drills, when removed, not remove their boxes. So you might have a few boxes out there waiting to be clicked away.