The first and easiest test is to pick up the turbo and shake it. If you have vibration issues and see the wheels wobbling in it and the turbine and compressor wheels don't spin at the same time, the best way to use this turbo is to put it in a nice box and throw it in the trash. The next step is the compressor wheel inspection. If you have any kind of bearing failure then most of the time you will also have compressor wheel failure. If you look here, you can see that the blade actually rolls up. This is because the wheel touches the shell back and forth. It could also be a soft damage issue.
If you pull in from the intercooler like a rag or a silicone coupler, it will also roll those blades back instead of breaking them, but usually you'll leave some shiny marks here like polish. If it has a lot of in and out play and a lot of axle play and maybe some bearing damage, the best way to fix it is to throw it away too. It might be hard to see in the pictures, but you can listen. It has a bunch of grooves and notches on the front. You can reprocess these and clean them up. Compressor wheels won't be too expensive depending on which one you get, but another thing you'll want to look for is on the very edge.
You should feel a smooth edge with your thumbnail coming off this corner here. If you feel any clicks, the wheel has contacted the housing. The best thing to do is to throw it away. Most bearing designs can take some left-to-right or top-to-bottom clearance, but when you have an in-and-out clearance if you look at the piston rings here, it's stationary -- the piston rings don't move, but the shaft Go in and out and cut out the grooves on the shaft.
Usually GT2056V Turbocharger 767720-5004S start having oil failures and it goes over the edge and the compressor wheel is just as bad. On the turbine and compressor side of the turbine's deflector, you'll see wear, and behind the seal gap, you'll see contact there. On the compressor side, you'll see damage on the bottom of the exhaust because the wheels are facing the compressor cover. There aren't many fixes you can do, you're better off buying new parts, but on the outside, visually you can't see the thrust damage going in and out, because everything is under the surface, so you really have to be careful about that.