BartHenry touched on that.. the way that generators can be remotely started varies, and i dont know much about that. I believe some you can feed a simple on/off signal to (which is what the dry contacts on the growatt provide) and some you need to have some kind of 'module' in between to manage it.
As far as sizing the generator, on my Growatt and possibly yours you can set a limit on how much battery charging current can come from the ac input, but you can't put an overall limit on what it pulls because it will pull those charging watts PLUS whatever watts your loads are. So whatever your max loads are in Watts, plus however many watts of charging you want to do while doing that, plus a huge fudge factor because generators have problems with 'surge' loads, is how big of a generator you should have. I have seen the most simplistic advice be to run a generator twice the size of your inverter. I doubt you want to run a 12kw generator, so the real solution is somewhere in between 6kw and 12kw based on how 'careful' you are ok with being, while on generator power. If you are REALLY careful about what loads you turn on and off, you can get away with a <6kw generator.