as you've have already mentioned suspected clutch issues and yes the only thing that can be wrong when you can select gears with the engine off but not with the engine on is the clutch
the first thing to do is bleed the clutch hydraulics and ensure that you replenish the all fluid in the system and get any trapped air out
I favour having a clear hose from the nipple to a jar 1/2 full of old fluid and with the nipple closed your assistant pushes the pedal up and down a few times, then holds it down whilst you then crack open the nipple and close it again whilst fluid is still flowing.
If you have difficulty getting fluid out then, on a lot of modern cars its far easier to use a vacuum bleed kit to pull the fluid through
If this doesn't help then next check the gear linkage for any worn bushes or pivots as any lost motion means reduced effort at the gearbox and replace as necessary. Ideally have your assistant move the gear lever with you watching the linkage and see if you can spot where there is any excessive play or lost motion.
If you still have issues with the hydraulics and its good after bleeding but then gets worse after a few days / hours, then I'd try leaving the clutch pedal held down overnight by bracing the pedal against the seat base with a piece of wood or similar, this is to try and force the seals inside the slave to take a set in the right orientation as over time they can shrink and dw air back in when you take your foot off the pedal.
This shrinkage isn't enough to leak any fluid but the gap is big enough to draw air in (gas being harder to seal than fluid) if this doesn't work I'm sorry to say that the slave cylinder is going to need changing.
also if the fluid is dark in colour this is a sign the seals are breaking up
Lastly if none of this helps then its possible the clutch is breaking up and no longer completely releasing and creating ‘drag’ - so in which case the transmission will have to come off to check / replace the clutch