The clutch, throughout bearing, pilot bearing and clutch adjustment fixed it.
I had a hydraulic clutch. There was an adjustment(s) either at the clutch pedal or the slave hydraulic cylinder. This was 15-20 years ago. A Japanese car I bought in 1982 and had for 17 years, 240K miles. One clutch I did. I was 250 miles from home, on vacation, but my uncle had the facilities.
I've never had a manual transmission apart, but you do have synchronizers that allow the gears to mesh. When mine failed like your failure, it was only reverse. The clutch I did heated up after 40 miles of high speed driving and would start to slip.
One failure was accompanied by a noise. They said the pilot bearing disintegrated.
If I remember right, as the clutch wears, you have to adjust the hydraulics, so the clutch disengages fully. So it could be there.
I'm pretty sure it was at both places (pedal and slave cylinder) At vthe slave you changed the amount of extension and at the pedal, you dampened the "bounce".