What that tells us is: There's a leak in the pipe between the control valve and the showerhead.
If the shower is on a tub and the leak does not happen when the tub spout is in use, then it's the pipe to the showerhead.
...and if there's only a showerhead, it's still the pipe to the showerhead.
In either case, you'll need to open up a wall and have a look at ...
What seems to have fixed the slow leak into the bowl is painfully simple:
Tighten the darn nut, but don't overtighten the darn nut.
Here's a picture of the bottom of the tank with the flush valve installed:
The instructions that came with the flush kit I bought suggest you tighten the flush valve nut (only) hand tight and warn about tank cracks if ...
If the leak is only from the tank to the bowl, and not on the floor, then the only option of the three you listed that can be the cause is the flapper.
Judging from the photo your flapper can be replaced without any disassembling of the tank.
There are two flexible tabs on the back of the flapper that go over two fixed pins on the bottom or the overflow ...
Moisture on below grade walls is common. The lucky thing for you there is not much depth there IF it becomes a problem.
Normally we put foundation drains in to drain the water away. This may not have been done since it’s not very deep.
If it becomes a problem it is fairly easy to put drains in or you may be able to have it done as part of the purchase.
This may be due to condensation from air infiltration.
Check that the refrigerator is level, or very slightly tilted back so that the doors swing shut on their own.
Check all door gaskets, i.e. they should be clean, flexible and seal completely on the entire perimeter.
Check that doors close completely. Adjust food contents, door hinges and anything else ...
You aren't supposed to use plumbers putty with acrylic tubs, the plastic washer does between the bottom of the tub and fitting(you can see the old one in the pic). Also the threads are supposed to be sealed with teflon tape or pipe sealant(non drying kind).
Finally many new tubs recommend silicone between the top trim piece and tub.
Your leak could be coming ...
I can't really tell from the picture, but the gasket looks kind of stretched out and I'd guess your leak is coming from it not sealing completely, not being located exactly right, or (perhaps because of the old putty?) the flange piece is not drawing down as tightly as it should to compress the gasket properly.
The gasket should be somewhat soft, elastic, ...
Plumber's putty is an old-school way of doing things. Any new hardware will have a rubber or neoprene gasket that goes between the tub and the fitting under the tub. The seal is actually underneath. I think I see it in your photo.
You may be able to just tighten things up better. A channel-lock or other plier with its jaws in the drain openings works well.
The threaded part on the valve where the hose connects seems, from the picture, to be rather short. It is possible that the part on the end of the hose is interfering with the valve body (represented by the green arrows in the diagram below) before the rubber hose washer gets a decent amount of compression on it.
If this is the case you may be able to ...