The parts you want must be available. Our local men's shed had green Nu-tools and yellow Axminster perform versions of this. I'm sure it's a generic design badged in many differnt colours. One died and someone sourced a new cast 2 part pulley that I fitted.
The lesson I learnt from stripping it down is that you MUST periodically lube the spindle where the two sides of the alloy pulley slide. It's a questionable design to need to lube a spindle inside a pulley where oil is at risk of being spun out onto the pulley cheeks where the belt rides, but without oil, the variable speed mechanism eventually gets stiff and gums up.
Over lube it and you'll get a belt soaked in oil slipping on the pulley. I've seen that too.
Keep hunting - I'm sure you'll find the part you need.