Synchronizer rings

I'd be more concerned about the tip of that shaft if that's wear pits and not junk on it.
Slider ring hub looks fine, but your critical parts are the condition of the teeth on the gears and syncros and if there is any play between the gears and shaft they run on. (like twisting it back and forth sideways on it's shaft)
Looseness between those is part of what makes sticks jump out of gear when accelerating or letting off.
The other is the angles on those teeth on the gears and the inside of the slide ring.
They are angled to increase the hold they have on each other under a load. (accelerating or decel either one)
When that angle wears it can actually force the gear and slides away from each other causing it to jump out of gear on acceleration.