Better Thermostate with external sensor and wax cartridges controlled by Shelly Mini G3

[crude pier]

I am trying to get my configuration working but probably messed up.
In our bathroom are two floor heating loops controlled by two thermostats that are in a different room. The reason for that was, that we intended to remote control these anyways and that saved a lot of pipes and work and money.

I changed the two room thermostats to wax cartridges and connected them to a single Shelly Blue Mini G3. The Shelly is available in my WiFi network and if I switch it on manually, the two cartridges start rising their knobs and hot water is moving through to the floor loops.

Then I added an instance of Better Thermostat and filled in the form as described in the docs on the BT homepage. For the temperature and humidity sensors I selected a Sonoff TH01 that is placed in the bathroom at about 1.6m above the floor.

Unfortunately now I have one instance of BT where I can turn the temperature dial derived from BT and another one derived from the shelly itself. The latter I can select the presets, but the dial is always overwritten to 26°C when moved.

None of the two instances ever switch the relay in any direction. When I manually set it to ON, it stays on, when I set it to OFF it stays off.

Did I miss something or is BT not compatible with my setup? I only found videos with relation to controlled valve type of TRVs or even Shelly TRVs but not the binary type I intended to use.

[crude pier]

Update:
The bathroom temperature regulation showed up in two thermostats. One initiated by the BT instance and one by the Mini Gen3 clamp.
So I made the BT one invisible. Then I enabled the relay by hand and let the room get warm. At the time the setpoint was reached, BT switched off the relay. It resulted in a 1.8°C overshoot but hey, that is fine for now.

Unfortunately this Sonoff TH01 temperature and humidity sensor failed again. No data, so the bathroom is again cold now.
On one hand it is one of the 1st generation TH sensors from Sonoff, on the other hand it has been parked untouched for 2 years, got a fresh battery and has a fresh firmware, so I am not very pleased with these. Hopefully the SNZB-02D are better in that job.

[crude pier]

Update:
I could not get the old little SNZB-02 to work ever again. I thought, when disabling the bridge and adding it to the Pro Stick, connected directly to the server, it would work. However I could not get it to pair.
The double pack of SNZB-02D arrived and I thought, I take the conventional way, registering them through the eWeLink App. For that I had to actiavte the ZB Bridge again. Okay, done. Scanned the code, updated the Sonoff Integration and the sensor was found.
I changed the sensors in the BT settings for the Bathroom and currently they are available. Need to wait until the temperature falling below the set point to see if the Gen3 Mini is then activated.

Now I try to activate the second SNZB-02D but even it was recognized flawlessly by the ZB Bridge, I cannot get it to show up in HA. Refreshed many times, no luck.

[crude pier]

Today we had an internet outage. Now the temperature and humidity sensor in the bath is shown offline. In ewelink the values are there. What is wrong with the Sonoff implementation?