I think its time to rebuild the front cylinder
At minimum, you want around 125 PSI
Hyosung says the limit is 110 psi hot and healthy range is 140 – 175 psi
Here is a cheap front barrel and piston, it should be OK
https://www.ebay.co.uk/itm/256864818680
And here is a spare one
https://www.ebay.co.uk/itm/255751060887
I have confidence that either of the above will finally get the bike running.
Ofcourse make sure to get new gaskets you see on this shop
Rear is already at the limit of 110 psi but… If you have to do the rear, then check these out
https://www.ebay.co.uk/itm/256513929819
Hyosung Korea isn’t making new pistons for carb 125cc or rings.
I am slowly researching and soon will test custom piston rings off another bike that may fit our bikes. If you just want piston rings, then i think you should email me , but stock is rare now.
This is why you can’t idle, the compression is too low.