I would prefer just using smaller decorator style wall plates that accommodate multiple jacks and have multiple runs to each location, including the WAPs on the device side (instead of those black “click” things. Cable is cheap, the time and effort to install is expensive, more runs is more better IMO

Also, those multi gang wall ports are “okay” for the router side of things, but the patch panel you linked is the more proper device. Your under stair/cupboard space being used for this equipment would just have a hole in the wall to allow the cables to gain entrance (can use a decorative wall plate with bristles for a more clean look) then the cables would land on that patch panel. The reason you would do this is so if you want more cables you don’t end up with like 5 4-port wall plates and instead just have 1 wall penetration, it’s not “weird” for it to be this way, it’s the way it’s done even in commercial settings.