The rules for Pokerstars Badugi doesn't state what bets are available. https://www.pokerstars.uk/poker/games/badugi/
Assuming it's BTN/SB versus BB and both decide to keep raising and calling if raise is not an option, how would the betting go? Assuming large enough stacks also. Observing a few games I believe it would roughly go like
1st betting round
BTN posts 0.5BB, BB posts 1BB
BTN raise to 2BB (putting 1.5BB in, +1.5BB), pot 3BB
BB raise to 3BB (+2BB), pot 5BB
BTN raises to 4BB (+2BB), pot 7BB
BB can't raise, calls (+1BB), pot 8BB
1st draw
2nd betting round
BB +1BB, BTN +2BB, BB +2BB, BTN +1BB (call) pot 14BB
2nd draw
3rd betting round
BB +2BB, BTN +4BB, BB +4BB, BTN +2BB (call) pot 26BB
3rd draw
4rd betting round
BB +2BB, BTN +4BB, BB +4BB, BTN +2BB (call) pot 38BB
Showdown