It could be a fault with the ACV (Air Cutoff Valves). They are called something else on the SV.
Parts 34 to 36 on here,
https://www.suzukipartshouse.com/oem...07f/carburetor
They enrich the mixture when the throttle is closed to prevent a weak mixture from causing popping when the the throttle is closed on CV carbs.
Also any Air-leaks into the carbs can cause your symptoms as can exhaust leaks.
If it is the ACV I think these are the ones but more research needed to confirm,
https://www.bts24.co.uk/en/engine/fu...ml&language=en