Just figured out it is for AC condensation from the new upstairs HVAC unit that sits above this bath. :-)

That it is

"Just figured out it is for AC condensation from the new upstairs HVAC unit that sits above this bath."

If that is what it is the connection is probably illegal under the plumbing codes.

You need an indirect wast with an air gap.

Using a DW Tee like that constitutes an indirect waste with an air gap, same as for dishwashers. That is why draining dishwashers gurgle in the sink drain.

arg! The plumbing inspector was just here this morning and did not have any issues with it BUT I wish I had been here to ask about it - i feel like I am a day late and a dollar short on this whole bathroom project. If code is not an issue, are there other issues I should be concerned about with this set up? thanks in advance for everyone's expertise.

It's fine, there are millions of installs exactly like it in the south, my Texas home has 2

The air gap is at the p- trap near the AC coil, or should be

"Using a DW Tee like that constitutes an indirect waste with an air gap, same as for dishwashers."

And that is not allowed in many areas.

The air gap for the DW is on the counter near the sink (and ugly).

If anything starts to smell in the drain line before the trap it can end up in the HVAC depending on how the AC coil is set up (input or output side of the blower).

The lines are vented post trap in the attics