Welcome!
If the fuel shutoff is leaking it may be sucking petrol into the right rear cylinder (that is where the vacuum to run it comes from) A bypass is the easiest fix, but there are some who prefer to keep it as one of Honda's failsafes (it also has a tipover cutoff switch so I think that the fuel cutoff is overkill) Not having the cutoff also means that if the bike sits for a while and fuel dries up in the carbs, the electric fuel pump will prime the carbs easier.
If the bike has been sitting around some petrol cleaner run through for a while and a good valve synch may be all it needs. After that there are a few long term maintenance items to look at, but I have had more trouble with younger cars than an older ST11! The ST11 is like a cattledog...not much work is no good, lots of hard work is better.