Manual transmission stuck in neutral

When you press the clutch and push the shifter to go into gear, does the shifter feel like it is being blocked from going in or does it move freely and just not go in gear?

These are two different issues that result in the vehicle not going into gear. The most common issue is that it feels like it is being blocked and that is due to the slave cylinder not fully separating the clutch disc and flywheel so that you can slide it into gear. Here is a guide that talks about this and replace the slave if that is needed:

https://www.2carpros.com/articles/throw-out-bearing-replacement

What happens when you put the vehicle in gear if the engine is off? Does it go into gear? Then lift the rear tires and start the engine or just pump the starter with the clutch in. Does the vehicle move or tires spin with the clutch fully depressed?

If it does then the clutch is not separating from the fly wheel and the slave/master assembly is the issue.

Please run through this and let's go from there. Thanks

It is highly unlikely that they put anything in wrong because with these there would be an issue almost immediately.

With the added info of hard to get it into reverse and now it will not go into gear it sounds like the slave cylinder is the issue. I would suggest just taking it back in because if they did happen to do something wrong then they will fix it. Otherwise, the slave cylinder will have a warranty on it, and they will replace it at no charge to you.

No matter what I am pretty convinced there is an issue with the slave cylinder. Clearly, I could be wrong, but it is not uncommon for new slave cylinders to leak.