Are you using it over Ethernet or WiFi? I remember I tried Moonlight to a local computer two or three years ago over Ethernet and the latency was still too bad, any ideas if that's better today?
I use Moonlight via direct 1 gbps Ethernet from a high-end gaming PC in the same house through a Google Chromecast 4K HDMI dongle with a powered USB-C hub for the RJ-45 input and it works flawlessly at 60 fps 4K 10-bit HDR with around 12 ms video latency. Some USB 3 hubs and USB Ethernet dongles won't reach full speeds on some streaming devices USB ports. The second one I tried worked at full 1 gbps.
You have to verify every software and hardware component in the chain is working at high-speed/low latency in your environment with a local speed test hosted on your source machine. I used self-hosted OpenSpeedTest. Moonlight works great but none of the consumer streaming stick or USB hub/RJ-45 dongles test for high speed/low latency across dozens of different device port hardware/firmware combos - so you can't trust claimed specs. Assume it's slow until you verify it's not.
UnRaid + KVM VM + GPU Passthrough with Moonlight has meant I no longer have to dual boot to game.
60FPS at 1080p on a 4k screen. 4k struggles but I think that's more my GPU then anything else. I do have 2x of them.
I'd say definitely give it another go.