This mower uses 2 different gearboxes for forward & reverse .
Both of them drive the same axle ( hopefully only one at a time ) part # 29 in the linked page below.
As it drives fine in reverse that leaves 5 possibilities for no forward motion
Part # 28 the forward gear box pulley is stripped on the shaft
Part # 31 the drive key is sheared
part # 22 the driven gear is worn or stripped
part # 26 the bevel gear is stripped
or the belt is slipping
Pull the cover off & watch what happens , could be as simple as the nut # 24 is not tight.
If the belt is slipping yopu should see , hear & smell it burning as it slips over the pulley.
If one of the other 4 you should hear a clicking sound as the stripped part rotates.
The drives themselves are interchangable as are the driven gears so you can swap them left right and see if the problem transfers to reverse .
Having gone through the difficult bit I would put my money on belt slipping as the mechanism that tensions the forward drive belt between will wear if the belt looses tension because of wear the small pulley will slip .
In particular check the tension pulley the pivot holes . That is part # 34 in the diagram and everything that is connected to it.
A small amount of ovality at the hole makes a big difference at the pulley.
Also check whatever moves 34 to engage the belt, usually there is an adjustment so you can select neutral .
Because it is used to drive forward most of the time you will get more wear on the forward parts.
IT could be as simple as swapping the tension springs over # 21 as the forward one will stretch .
Or as the axle seems to be moving the circlip part # 32 may have fallen off or even been forgotten .
Good news is all of the bits seem to be available and reasonably priced.
WAW 34 parts diagram from Jacks.