This is the way.
Done correctly, all of the devices will be on one network (i.e. they can all see each other, and there is a single device - the primary router - that is providing NAT/DHCP services to all devices), AND there will be two wi-fi options in the house with two SSID’s, one from the primary and one from the secondary. So you would get the benefit of a faster wireless connection for the Quest.
One minor question for OP: do you really need the secondary router and that network switch? I would guess the secondary router would have enough ethernet ports.
I am in the same boat as OP — can you share any advice on where to look, and any examples of different brands, models, or specs to look for to make sure I’m not buying crap?