Morning all.
Do the tickover/throttle cable adjustments as suggested & see how it goes.
Severely out of balance carburettors or throttle bodies would cause a missfire when the idle drops, as effectively one cylinder will start to cut out as it's air supply is lost
Despite the SV being one of the easier bikes to balance (apart from access to the adjusting screw on carb models) I have seen plenty where the owner or a previous one has got 'twiddlitus' & messed it up. Probably form trying to do it by ear!
Cheers.