Zigbee mesh connections?

Theoretically yes, because Z-Wave uses a lower frequency (868,42 MHz in Europe) than Zigbee (2,4 GHz) and should therefore (theoretically) have a longer range.
Homey Pro (early 2023) uses a Z-Wave Plus chip of the 700 series which has a higher range than the older Homey models or other chips like 500 or 300.
So if you want to try out Z-Wave devices, you should use those that use at least a 700 or 800 chipset. Devices with an 800 chipset are downward compatible.

But, besides the problem that the Zigbee devices may not automatically search for a new route, I think another big problem is that you simply don’t have enough Zigbee routers (plugs, lights, and other permanently powered devices). And this could also be a problem for the Z-Wave devices.

Is it not possible to install an outdoor WLAN repeater in your pump house or greenhouse?

Yeah maybe the jump from the indoors plug to the pump house plug is just too far (even though I could control that plug), unfortunately there is just no way of adding a router in between them (there is no electric wiring available and even if I added some extension cord, they would just be covered in snow during winter anyway)

Unfortunately not, I have already maxed my Orbi mesh with 3 extra satellites (basement + upstairs + garage, router sits at first floor). I could maybe add an AP by using a CAT7 cable over there but getting it there would be non-trivial due to the layout of the garden (lots of water features/flower gardens and wood decks etc) so its not really an option, thus my idea of using zigbee routers to bridge the gaps :confused: Also, I guess that would create a separate network, not sure how that works for the Homey when devices are scattered across multiple networks.

Btw, WiFi and Zigbee can interfere with each other, because they operate both on 2.4 GHz.
You can check if there may be a problem on this page:

https://ostgardh.se/wifi_zigbee/

The Homey Zigbee channel can be found in Developer Tools → Zigbee → System Information.
The Zigbee channel of Homey can’t be changed manually. Just with a Zigbee Network Reset it search’s for a “optimal” channel.
So the better way is to adjust and fix the channel of the 2.4 GHz WiFi Network.

No collisions there, zigbee is at channel 25 and wifi uses 3 and 7.
Not a crowded wifi here in the outbacks either, only one neighbour has wifi that overlaps somewhat, but not in any major way.

I was thinking about a greenhouse, made of aluminium, is probably acting like a Faraday’s cage?
It can seriously ruin your zigbee signal.

So I suggest to (temporarily) add another router device on the outside, as close as possible to the greenhouse.
Maybe that’s júst about enough to get the transmitting and receiving signals in and out of the greenhouse.

We built it from wood and single pane glass windows so it shouldn’t reduce the signal in any meaningful way.

The same goes for the pump house, it’s built from wooden planks (even has gaps between the planks for air flow) that are 22mm thick so it shouldn’t reduce the signal that much either.

So for the outside, its basically free line of sight between the plugs.

When I stand in the greenhouse i mostly have connection (very weak though, but still) with our wifi on my phone and since it is the same frequency as zigbee and the router sits at basically the same spot as the zigbee router/plug in the house, the zigbee signal really should reach the pump house without an issue and then have no issue connecting with the plugs in the greenhouse (since its a shorter distance and free line of sight) so its most likely something wrong with the zigbee plugs, as robertklep suggests.