what impacts the sound quality more amp or pre-amp

would a moscode 300 hybride tube amp pair well with my system?

It would drive your speakers, but seems like a lateral move from the B&K, I would also worry about such a old amp unless it gets the once over by a tech and possibly its capacitors replaced - it is a early 80s amp - no?

Could you describe what it is that you are trying to change with the sound of your system? Something you don't like about what you currently have that you are trying to improve? That B&K amp is a pretty nice SS amp.

looking to get more silky mids and highs, larger soundstage.. the original chinese tubes in the jolida were nice but too loose in low end

I think you would be well served by trying the Mapletree Audio preamp previously mentioned $760 new, $800 with Blackgate Capacitor upgrade (Made by a retired E.E. Professor/Audiophlie in Canada). I think you would get the kind of change you are looking for as you described it. Do you know the input impedance of ST202? Should be OK with the Mapletree unless less than 20kohm. The Mapletree is wonderfully smooth and full of tone with its use of the 12sn7 or 6sn7 tube.

My memory could be failing me on all this, I could be mistaken, but if I recall correctly the B&K's ST series, had a rather low input impedance, and a low V input sensitivity for full output. Both of which can make matching a tube pre to a bit tricky. Another concern might be the ability of the B&K's non + ST series of amps ability to handle 4 Ohm loads well.