...... But I think the fork is out of its place.
.... or the whole input shaft has somehow moved backwards a couple mm??
Before you pull apart the whole TC, here are a few dimensions you can check and compare with yours, after removing that top 4-bolt cover (plus the poppet ball, stem & spring) ....
- For fairly new parts, the synchro collar is 17.5mm thick and the groove in the fork is 18.3-18.4mm wide. So there you have a total play of 0.8-0.9mm. It can be felt by moving the shift shaft in-out. (it appears to be more than that, in this pic, but it really is less than 1mm)
2. Free (back-forth) movement of the whole synchro unit is little over 2mm, between both gears. Past that, you start compressing the spring-loaded clutch collar of the synchronizer.
3. Total travel of the collar - out of neutral, and up to complete engagement, after stopping against the gear's face - is about 14mm. The synchro itself allows for 15mm travel of the collar, each way. Synchro- and gear dogs start making contact after the first 5mm of travel.
4. With the fork perfectly centered in Neutral, the distance measured from the backside of the fork to where it would contact the housing is ~20mm. So, if all was normal, there is plenty of room left for a full engagement, without the fork touching the case.
5. With the set screw tightened in place, the distance between backside of fork and first groove of shift shaft is ~19mm. (below pic) That means that when the shaft/fork assembly is in Neutral, that first groove should just appear visible, out of the bore in the housing.
I would also unscrew the set screw and check that it is in good shape. Compare with pictures below.....