Crosstalk Solutions has a couple of videos on similar setups: Log Cabin Property and Greek Port. Good tips on how to design it using Ubiquiti’s free tools too.
You’ll need a point-to-multipoint setup with APs as rebroadcasters. Just having a powerful central antenna is no good because the antennas in the client devices are your limiting factor.
I have used Ubiquiti for my home network for years, and it has always worked great at what it promised to do for me. People’s frustrations with it—in my experience—usually revolve around things they want it to do that it doesn’t, and the fact that it is very unfriendly to hacks or jury-rigging. So you have to be very sure going in that it matches your requirements. It’s like Apple gear.
Another option you could look at is TP-Link’s Omada system, which is basically their clone of Unifi but has a wider variety of hardware options.
I also often see people using Ubiquiti switches and APs in combination with a pfSense firewall if they want more sophistication and configurability. If you’re coming from Sophos and want to do sophisticated routing and filtering, you’ll probably find the Unifi firewall lacking in features (but it works great for people who don’t want to do that).
Return it. Buy a Cat6 cable and an unmanaged switch. Ethernet splitters are a scam, and Cat 8 is a cable for special applications in big data centres and nothing you own can take advantage of the ways it differs from regular Cat 6 unless you’re Bill Gates.