Leak Detection

By checking each fixture independently you will acknowledge one of two things:
the leak happens only with one fixture or worst case scenario it occurs both times in which case the leak will be on the drain after the two have been tied together.

Probably by now you should be opening the ceiling near the leak to find the actual drain. Boil up some water and pour it into either the sink or tub and feel the drain pipe to determine how far it travels before the pipe remains cool.
Once you have established this you at least know where the blockage is and perhaps a poor or worn joint is allowing the water to spill out.

In the event that there is no leak detected at all when draining water then your issue is with the supply lines for hot and cold but the leak would then be a constant stream of water with plenty of visual damage which is progressively getting worse.

We wouldn’t wish that on anyone!