It's murky because these terms are mostly fan-governed. GF/Nintendo has used them from time to time, but there's isn't really a hard line, or even a need for one. It's fans who give these terms power. Same as the idea of a 'generation' - we can argue all day about if this is gen 7, gen 7.5, gen 8 or completely separate, but does it even matter?
The problem is that these terms worked very well in the past because things were very clear cut and formulaic. We could consider games "main series" because they always followed a very predictable formula. New installments have different bells and whistles but the base experience is the same. They've gotten a bit bolder with time, first adding bigger bells and whistles (mega evolutions, etc) and then going as far as to ditch gyms for a little while.
I'd say that Let's Go is a continuation of that trend, a genuine effort by GameFreak to create something different than they have before. I don't think that makes it a side-game, but again, definitions don't really matter.
I guess the concern is that if it's a main game, so to speak, then the ideas it introduces could seep into future games. For better or for worse, I think this is inevitable either way. If the game is successful and people enjoy it, they will continue those ideas. It's being made by the developers of the main series, so even if you don't consider it main series, they're taking notes.
Which of course begs the question, if you call it a side game now, and then gen 8 comes out with all these fancy new Pokemon but still has no wild battles (etc), and then every other new Pokemon game follows suit, will Let's Go then become main series? :)