Basment Bathtub vent question

I am working on my basement bathroom, and very new to this stuff, but i'm stuck thinking about the venting options for the tub. I have a couple questions and I've attached a quick drawing of what I have.

1. Is the tub line already vented perhaps along with the toilet stubout, or not?
2. Can i tie the wetbar drain into the same drain as the vanity? I have the wetbar sink venting with an AAV which is permitted in my area, so I don't need to worry about venting that.
3. If the 2" line under the concrete does need its own vent, how can I tie into the 1.5" vent stack that's there? The wetbar drain line in in the 2x4 wall, so I can't go around it and up into the vent line?

Or perhaps I should drain the wetbar line and the tub both into the 2" tub drain and that will clear a path to get to the vent? Any thought would be appreciated. Thanks in advance,

Hopefully the pipe coming out of the floor to the lav is 2", because a 1-1/2 should not be run underground.
If so, the 2" shower/tub drain and the toilet MIGHT be wet vented through the lavatory.

Finding out how is was installed is a problem. If you cannot confirm the original installation through the builder, you might have to open up the floor to see what is there.

Yes, where it comes out of the floor it's 2"; it reduces to 1.5" at the cleanout. I should have noted that dimension on my drawing. Is there a way to test if its wet vented without digging all the concrete up? e.g. put a ptrap in the hole and pour water down? If its vented properly i would think the water would pour through without issue. If not, wouldn't I see it trying to gulp air through the ptrap and maybe smell sewer? Maybe that's a stupid question.

Maybe I'm better off just to vent the tub line anyways? The room next to this, behind the wall with the pipe in it, is my mechanical room. I guess I could just pipe through there into the vent or use an aav...

You could have a plumber run a camera down the lines to see how the connections are made, I couldn't say for sure what he might be able to see with the camera without trying it.