There are three parts to a working Hive system. The thermostat (as in your picture), a receiver that connects to your home router and a hub that replaces your existing central heating programmer.
https://www.amazon.co.uk/Hive-851814-Thermostat-Heating-control/dp/B097TNDW6Y
Presumably before you started the system was working correctly with the Danfoss and your only change was to swap Danfoss to Hive. Are you able to re-instate the Danfoss to verify the central heating is OK?
When you said "did exactly what you said" does that mean the link between 3 & 6 was not...
looking at your original picture for the Danfos 102, I think you had
T1 - 1 x brown
T2 - 1 x brown
T3 - 3 x Earth
T5 - 2 x blue
T6 - 1 x brown
link between T3 & T6 - blue
Your Hive picture shows
N - 3 x blue (from T5) <<====
L - 1 x brown (from T6)
3 - 1 x brown (from T1)
4 - 1...
Sounds like it's working correctly. If pressing the HW button on it's own fires up the boiler that implies the hot water tank is below the thermostat temp. Then when you press the CH button, the boiler fires up because the hot water is still below it's required temp. In gravity mode the HW is...
You should swap for Kit-1
If you have problems swapping at Screwfix and your boiler supports 240V switching, it may be possible use the 2-channel model leaving the Wiser hot water channel unused. However you should attempt to replace as that's the best way forward...
The Wiser would generally replace the existing programmer rather than thermostat.
How do you currently manage the on/off periods for hot water and central heating.
Also note the Hive internet hub uses an ethernet port on your router or switch. I'd recommend you review the differences between the Hivi mini (£108) and regular Hive (£150). The Wiser 2-channel model is also around £150
On that basis you should just be able to swap over to either Hive or Wiser. Both use an identical wiring arrangement to what you have today. You may even be able to reuse the current ST9400C backplate but even if not it's a simple rewire.
Just ensure you get the correct model, you will need one...
Do you have a separate pump for the UFH or is it shared with the HW & CH? If it's shared, that implies the boiler controls the pump. Excluding the smart side of the Wiser, in essence all its doing is applying 240V to the brown wire into the 2-port valve. The valve orange connection should not...
If you have a mid-port valve that implies Y-Plan. Presumably you have independent control over HW and CH, some Y-Plan systems require HW to be on to allow the CH to run. As for proprietary systems, they are all to some extent if you tie in their smart TRV's, light bulbs, etc. If however you are...
You indicate your current system is HW/CH. Is your hot water pumped or gravity feed. Your best bet would probably be Hive or Wiser to replace your ST9400C. However prior to deciding you need to understand your type of heating system. For example Hive supports gravity HW whilst Wiser does not...