To be perfectly honest, I'm more drawn to this statement when it comes to you inquiring about temperatures: "...and there is also an UTH which is simply plugged into a socket." An unregulated UTH will be much more of a threat to your eventual new addition than being worried over a couple degrees of ambient temperature. I would move your Inkbird thermostat probe to be in direct contact with your UTH (sandwiched between the mat and the glass if possible; if not possible, then taped directly to the underside of the mat) to control the heat mat and use a rheostat/dimmer switch to control the light bulb. You'll end up with safer temperatures and extend the life of both your heat bulb and your animal.
And, of course, a good visual on how to properly use a thermostat to control a UTH:
This is very detailed, thank you! I’ve honestly been considering getting a splitter the thermostat plug so it can occupy both the heat lamp and the UTH. Would that also be a good step?