Replacing bathroom sink popup drain if sink has hairline cracks

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.

Assuming there are no other drain problems occurring (because you did not mention any) you most certainly have an obstruction of the branch drain line leading to that sink.

Option 1- run a good quality drain auger down the drain, through the trap, and down the branch line as far as it will go.

Option 2- take the trap back apart and run the cable directly down the drain line.

For either option, it is important that you use the correct technique and persevere until the length of the cable has gone down. It's not easy, be prepared to work. There are numerous instructional videos on-line, this one shows the correct technique but the person is using a cheap sub-standard auger.

I always cable from the top and run water until it backs up a bit, so I can tell when I have hit the clog (because the water suddenly drains). I highly recommend that you invest in a good professional quality auger, I did and it has saved me hundreds and hundreds of dollars over the years:
Always wipe off the cable with a rag as you remove it from the drain, and always spray it down with your favorite water displacing spray lube that comes in a blue and yellow can or it will rust in the drum.