I have a small 4- story house; how many Homeys do I need?

Garage is downstairs, ground floor is living area and kitchen (and where my internet modem is), first floor had two bedrooms, second floor another bedroom.

How many Homeys or extensions do I need?

1 Homey and properly chosen mesh devices - Z-Wave/ Zigbee (or all Wifi if that’s Okay) - it always depends what you want to achieve

Maybe this is a silly question, but how does the signal get from one floor to the other in a 4-story home? Mesh devices, I get that. But that still doesn’t answer my question. Or am I overthinking this?

The zigbee signal is not in a flat horizontal circle, so it reaches up- and downstairs as well.
When you’ve reinforced concrete floors, try to position the zigbee routers near the stairs.
It’s experimenting a bit, when the zigbee devices start to act flaky, the distance between the routers is too big.
I can say I have r. concrete floors, and the zigbee signal reaches upstairs just fine by not doing anything special.

That is a question that has ‘if’ beyond all responses. Maybe you can do it with one, but I suspect you’’ll need two. But the Z meshes might work well with just the one. Try it and see.

You are overthinking this, if you use enough router devices like lights or sockets you should be ok. I have one homey and 300+ zigbee devices scattered across 4 floors, the garden and the shed in the back of the garden and no problem whatsoever.