I have and use Sonoff RF Bridge (hardware modded with OMG Pilight), Digoo R8H, Arduino MEGA(with RFLink) and Wemos D1 mini (with OMG RF).
As far as I know, currently you can not get readings from R8H using OMG, it only works with RFLink.
So if your goal is to use R8H, then you need a board flashed with RFLink and not Sonoff RF Bridge. There are ways to connect RFLink via WiFi as pointed out earlier.
If you don’t care if it’s R8H or another sensor and all you need is temperature/humidity readings via MQTT, you might be better off building something like BRUH sensor - possibly using Wemos D1 mini and flashed with ESPHome (I believe there are plenty of options and guides around). That way you don’t need Sonoff RF bridge as your sensor will use WiFi, not RF signal to transfer data.
Another thing - don’t use Digoo R8S unless you’re going to power it from a power adaptor as it will change its ID every time you replace batteries and it sucks.