I guess you don't see water dripping except very little because the water was absorbed to the wall.

The dripping probably just from cover. Did you check how much water from the dripping?

Most likely the cover is not water tight, not screwed properly or no seal. Need to reopen and close properly. I guess it was just screwed by hand but if tight need to use tool to open like big mouth spanner.

The floor concrete normally mixed with water proofing material nowadays. Last time probably just water proofing an inch layer of cement before tiling. The wall side some would just paint water proofing material several inches from floor. Probably was not done. Normally the leak at corner or joint where wall meets floor concrete.

Normally the basin drainage end up together at the floor drainage ... so color become brown?

Why not. Simple job. My grout has become yellowish and moldy

If I were to re-grout, I'd go for silicone

Normally inside the wall and flooring itself. After the trap, no need to expose anywhere else. However, since it also has joint along the way, leak could be there.

Anyway, the water from sink will flow fast through outlet. Can't detect anything unless you can plug before it merge to floor outlet. BTW, your leak now is on flooring

Since you did ponding test, the leak is nothing related to sink .... right?

I presumed must be floor related or point where wall meet the floor concrete slab.