Seal bathroom sink drain to vanity/wall

This might not be the answer, but for reference here is a problem that can occur if the plumbing is not installed properly.

If you look at Fig. 3, this is what a proper drain looks like. You'll notice the orange line represents the water level in the system, the water levels out in the trap preventing sewer gases from entering the sink drain.

In Fig. 1, you can see what will happen if the drain line has to go up before meeting the main drain line. Again the orange line represents the water level in the system, and as you can see the water level is much higher in the drain.

Fig. 2 shows what could happen if the sink was installed lower than the rise in the drain line. The water would never fully drain from the sink, since it would require extra pressure in the system to push the water up the drain.

I wouldn't guess this is the issue in this case; since as you can see, if you opened the trap in this case you would have more water drain than what is typically in the trap.

In a perfect world Fig.1 and 2 would never pass inspection, but as we all know not all plumbing is properly installed and/or inspected. So this could possibly be the case in this situation (given the plumbing was installed by an amateur plumber), but it is doubtful. It would be more likely caused by a clog in the line.

Assuming the waste line is still at the proper angle (it does need to have slight decline or gravity won't work for you):

It sounds to me as if you have an airflow problem in the vent stack. There must have been some reason you changed the connection between the drain and the waste stubout? Was something slow before that? Or was there a leak? It's possible something (leaves, dirt) got blown in through the top of the vent stack. Or perhaps it got jostled somehow. If you had positive or negative pressure building up in the pipes due to a lack of airflow, that might have been causing other problems.

Waste lines need to be attached to a waste vent in order to maintain neutral air pressure in the pipes so that the water will flow out due to gravity. Otherwise as the waste water flows in it puts pressure on the air in front of it, which pushes back against the water...causing it to drain slowly or not at all.

Typically the sink waste line is connected to the toilet waste line and that is connected to the vent stack. If you don't have a slow toilet as well, perhaps you have just enough venting to handle the toilet flow but not enough to handle the sink.

If you are in a single family home, the vent stack is probably up on the roof. I believe universal code is or used to be that the vent stack has to be within 5 feet of the waste pipe, so look directly above wherever your slow sink is. You need to go up there with a flashlight and see if you can find any blockages at the top of the vent stack (leaves, dirt, other junk). Towards the top you can stick any kind of long pole in there and try to dislodge any partial blockage. If there is a blockage farther down then can also run a garden hose up there, feed it down through the vent, turn on the water and try to blast out any blockage, which should just go back down and into the sewer.

If that doesn't work something might have put a kink or something in the vent pipe and you're probably going to have to call a pro unless you want to start cutting into the wall to get access.