The belt does not look to me as if it has been bottoming in a pulley: no shiny marks on its underside. However the teeth on the ratchet bar do not look all that good. See this thread:

https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=43216#Post43216

We have had one case where the ratchet was not holding, so the pulley could slip backward under load:
https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=39126&Searchpage=1&Main=7408&Words=%2B+%22angle+grinder%22&Search=true#Post39126

I suggest you check whether you can pull the spring-loaded tensioning pulley back against the ratchet (the problem Nooni had). I'll try to explain how this could cause belt slip when moving forward but not backward. Here is a marked up version of one of your pictures:
[Linked Image]

The green arrow, pointed toward the front of the machine, is on top of what I believe is your forward clutch. The belt would be moving forward there, and backward over the other (reverse) clutch. Remember that the forward clutch pulley is rotated by belt tension, so when moving forward the belt has no tension upstream of the forward clutch (up toward the engine pulley), but a lot of tension in front of the clutch pulley, toward the idler pulley. That belt tension is carried around the idler, around the reverse clutch, and forward to the engine pulley. The result of this is that the idler is being pulled backward by twice the belt tension, whenever you are moving forward. (The belt tension is the same on both sides of the idler.) That is quite a large force trying to pull the idler back, whenever the forward clutch is engaged. If it weren't for the ratchet system, the idler would just move toward the back of the mower due to that force, slackening the belt and causing the mower to not move at all. Conversely when you engage the reverse clutch, there is virtually no tension in the belt upstream of the reverse clutch pulley, and hence no backward force on the idler pulley. Thus when you reverse, the idler pulley has the chance to move forward under spring pressure and engage the next ratchet position, to compensate for belt wear. Hence, when a Greenfield will only move backward, not forward, the first thing to suspect is that you have Nooni's problem: a slipping idler ratchet. If the idler ratchet is OK, and you have pushed the idler forward as far as possible so the belt is very tight, there seem to be only two remaining possible causes of the lack of forward drive. The first is that the belt is touching the bottom of a pulley, so it can't jam in the V pulley and deliver some serious driving torque. It would most likely be the engine pulley that it was slipping on, and the cure would be a new belt. The second possible cause is that the forward clutch is worn out and is slipping. Generally, a slipping belt squeals, while a slipping clutch makes less noise and at a lower pitch.

So, I suggest you look at the idler ratchet to make sure you don't have Nooni's fault. If that is OK, look at the engine pulley that drives the wheel belt, not the cutter belt, to see if the belt has been touching the bottom of the groove. For Pete's sake disconnect the spark plug lead before you get under the mower to look at that pulley.

If you can convince yourself that you have plenty of belt tension, the pulley is firmly locked by the ratchet, and the belt has not been touching the bottom of the engine pulley, you'll have to think about a new forward clutch lining. That is not a very big job on your relatively recent-model Greenfield with its short clutch shaft, but it would be a pity to do it if there is nothing wrong with the clutch lining you have at present.