Throttle does not snap back [Urgent :/]

Something else to consider, and I'm not sure if it applies with your bike but you should check how tight the kill switch hand controls are. Sometimes if you screw them too tight it will not allow the throttle (hand controls) to fully close. It sounds silly but losen the screws just a tad and see if that has any impact. If not, no harm no foul.

Remove the cables and actuate the throttle on the carbs by hand. If they operate as they should, reinstall the cables loosely.

The manual is confusing on the adjustment procedure.

Tighten the pull cable until you have 3mm or so free play. Then tighten the push cable until the throttle begins to return slowly. Back off on the push cable until it operates as it should, snapping back still with the slight freeplay, and tighten it up.

Fixed! I'll be posting a short video soon, it was not any cables or any of the sort, instead it was the aftermarket throttle grip binding against the right hand side control box (engine start lights etc). I removed a small rubber gasket and it works perfectly. Thank you everyone for your help!!

First thing to try is disconnect the push cable completely then see if the carb snaps back as it should. My guess is it will work fine without it. So at that point you can fight for hours figuring and trying every conceivable setting to get the cables to jive, probably in vain, or just run the main pull cable and forget the dumb push cable. Of course this is illegal and dangerous though. Having carb work fine by disconnecting any safetycrat feature not recommended.