[Spring44]

Maybe bad syncros in the transmission or maybe the clutch is not disengaging completely during shifts due to a failing hydraulic clutch master or slave cylinder.

You should hope that it is clutch hydraulics failing, because that is easier to fix than replacing syncros. I think that this is more probable as the cause than bad syncros, unless the PO really abused the transmission. Good luck!

To test, start your car and at idle push in the clutch pedal and engage each forward gear, then engage reverse. If the forward gears can be engaged with little or no grinding, but reverse grinds, that is an indicator that the clutch is not completely disengaging. Since all of the forward gears are synchronized they will tend to go ahead and engage with little resistance. But reverse is not synchronized and it will tend to grind because the clutch is not completely disengaged.