Hi @Antohind yes you certainly can do that, I am doing it right now in my home lab just as a test.
What you are basically describing is the WGB Workgroup Bridge scenario, using a wireless mesh link between the house and garden office and it sounds like you'd have a switch in the garden office which connects to the server and also connects (and powers) the AP. You would have both APs in the same wireless network in Dashboard and they'll automatically form the mesh link if they're within range of one another. Also remember there's always a performance impact associated with mesh/repeater links, so try some throughput tests to get a baseline.
Just to clarify because the terminology is sometimes confusing, in the Meraki documentation we refer to them as "Mesh Gateway" APs (have a wired Ethernet backhaul connection, like in your house) and "Mesh Repeater" APs (only have a wireless backhaul, like in your garden office). These terms are sometimes shortened to "Gateway AP" and "Mesh AP" respectively. And sometimes “Mesh AP” is synonymous with “Repeater AP”. This is discussed in the first link below.
You can have the mesh AP provide wired connectivity to clients (which is the WGB, WorkGroup Bridge type functionality) and also serve WiFi clients on its wireless radios (which is basically the Mesh Repeater functionality). If you wanted to have wired clients + additional wireless APs in a remote office/building across the park, then you would need a Layer 3 switch as mentioned in the KB article below. This may not apply (for now) since you’re looking to do straight up wireless mesh. But when that time comes, check out the wired LAN extension article (2nd link below) and the "Extending the LAN for Wired Clients" image of that KB article. You would configure your APs in Dashboard accordingly with an SSID in Bridge Mode, and update the setting to allow clients on the wired interface to behave as if they were connected to the Bridge Mode SSID.
When you first connect the Mesh Repeater AP across the property, to speed things up you might want to just use an AC power adapter and not have it plugged into a PoE switch on its Ethernet port. If it's wired it may take longer, attempting to come up as a Mesh Gateway AP instead of a Mesh Repeater AP. So once things are configured in Dashboard, if you just give the Mesh Repeater AP (garden office) power and its within range of the Gateway AP in the house, they'll automatically mesh up. Now, if the Mesh Repeater AP has never been powered up before and was never connected to a wired network, it can take a while longer to come up. Give it time to complete everything, during which time it will likely be alerting and indicate certain errors regarding connectivity in Dashboard. I’ve done this in my lab and Dashboard did cycle through a few different seemingly odd warning messages over 15 minutes or so, but then settled down, went green, and then stayed rock solid.
Also see the article below on manually changing channels in a mesh network and using a Meraki AP as a repeater. You actually cannot control which radio 2.4GHz or 5GHz gets used for the wireless backhaul bridge link. I'd say that's because it's all about simplicity, Meraki was born out of an MIT research project for outdoor wireless mesh and needed everything to be plug and play, so the APs will automatically choose the better performing radio for the mesh backhaul. In fact, you can also even serve clients on the same radio used for the mesh backhaul, although that's not desirable. So what we can do is use with outdoor APs is use 5GHz-only sector antennas between the Gateway and Repeater APs to make sure the 5GHz band used for the backhaul (best practice) and use omnis to serve clients on the 2.4GHz radio so they don't impact your backhaul bandwidth. The other thing you could do (assuming you have indoor APs) do is manually set the 5GHz radios to be on the same channel and then 2.4GHz radios on different channels, then the APs would really have no choice but to mesh up on 5GHz and clients could connect to 2.4. This is discussed in the 3rd KB article below.
Here's all the supporting documentation.
Looks like a lot but only 1-2 pages each:
Cisco Meraki Gateway AP vs. Repeater AP:
https://documentation.meraki.com/MR/Other_Topics/Cisco_Meraki_Gateway_AP_vs._Repeater_AP
Extending the LAN with a Wireless Mesh Link:
https://documentation.meraki.com/MR/Other_Topics/Extending_the_LAN_with_a_Wireless_Mesh_Link
Using a Cisco Meraki Access Point as a Mesh Repeater:
https://documentation.meraki.com/MR/Other_Topics/Using_a_Cisco_Meraki_Access_Point_as_a_Mesh_Repeate...
Manually Changing Channels in a Mesh Network
https://documentation.meraki.com/MR/Radio_Settings/Manually_Changing_Channels_in_a_Mesh_Network
Sorry about writing a book here - you asked what time it was and now you know how to build a watch! haha. I had most of that in bits and pieces across a few emails so it was easy enough to copy/paste. Hope it's helpful and good luck!