It sounds like engaging the clutch is not fully disengaging the gearbox input shaft from the flywheel. There could be multiple reasons:
– the pressure plate is not being fully employed. E.g. the clutch slave is not moving the throw-out bearing arm far enough, or some other reason.
– the gearbox input shaft is binding in the pilot bushing in the flywheel
– the clutch disc is sticking to the flywheel

This past winter, I replaced my gearbox, clutch disc, pilot bushing, and rebuilt the clutch hydraulics. My car sat a few months more while some other work was finished up. When I finally got the car running, I had a similar issue. I could not get the gearbox into gear with the clutch depressed. I thought maybe the clutch parts were binding from sitting a while, so I tried a simple test. I applied the handbrake fully, blocked all 4 wheels, opened the garage door and made sure the area outside the garage door opening was clear. I applied the clutch, selected reverse gear, then I started the car. I felt the car wanting to move a little bit upon starting and for a few more seconds, but the car remained in place. Then I revved the engine a bit to 2k – 2.5k rpms. I then put the gearbox in neutral and disengaged the clutch. Then I was able to apply the clutch and select any gears without grinding.

So in my situation, I had some minor binding of components and I used the starter to break it free. I think my clutch disc was sticking to the flywheel after sitting for a while.

I think you can try this test to see if you have minor binding of components. If you can’t get the car started with this test and/or the car is lunging, then it would seem more likely the pressure plate is not fully releasing the pressure on the clutch disc.