I think your diagrams say the spot of the leak is higher than the lavatory drain and the water level in the toilet bowl. Yet water is not rising in those. So if there were a blockage causing water to rise, it would rise in the lavatory or toilet bowl.
Water is not going to be sucked up against gravity in a home.
So my suspicion is that water is coming from above, and maybe over the outside of the pipe, hitting the top of the tee fitting, flowing around the back of the tee where you see it. That is why the suggestion of cloth strips -- to intercept the water coming down the back side of the pipe and let it be detected.
If water is not coming from above outside the pipe, that would imply both a blockage in the vent line below the cross, a blockage in both side legs of the cross, and a source of water above inside the piping. That could be rain into the top opening of the pipe, but three blockages? Seems to be highly improbable. Plus, it had not been raining recently.
One potential source of water is that sometimes people drill a hole in a vent and inject condensation from an attic air conditioner. I don't think that is likely in NY. Plus, you would have seen that and mentioned it.
The other source of water would be condensation. For condensation inside the pipe, I would expect the the pipe to be cooler than the air inside. In the winter, I would expect the air in the pipe to be cooler than the pipe. So that seems not so likely, it seems possible.
Usually with PVC, there is a purple primer used during the gluing process. Clear primer exists, and it is possible that was used. Do your other fittings show purple primer? If water is not coming from outside, that means a bad PVC joint that lets unpressurized water flow through. I don't think that is at all common, but I have limited experience.
If you are convinced that the water is coming from inside the pipe through a bad joint, you could try a Leak-B-Gone PVC Repair Ring, or replace the tee. Another option would be to dry the area, build a dam of some sort, and pour epoxy glue to encapsulate the leaky joint. Another option is to use a few layers of good self-fusing silicone tape, topped with another tape that will provide some compression. Scotch 66 or 33+ electrical tape or Scotch #35 Electrical Tape, White pulled moderately tight might be good for the outer wrap. The white would look better.