Which has a greater influence on sound quality, the amp or the preamp?

Yes, but there is always a point when it is time to upgrade speakers too.

I may be wrong but I have an impression that quite a number of audiophiles use different brands of preamp and power amp. Many also think that it is in fact more difficult to make a great preamp than power amp. Besides, synergy doesn't mean it must be one brand.

Well, sound preferences differ, so do preamps. As far as I know, most audiophiles do have active preamp in their systems. Going direct can give more pure but less refined presentation.

You may not need active preamp in the system but you will always want it, whether you know it or not.

Yeah, balance is the key. And speaking of tube equipment - tubes matter, a lot.

It is probably impossible to beat a great tube preamp.