How does climatization affect my score?

Yap, any use of climate system, heat or cool or dehumidify, will lower your ECO score and affect the EV MODE AC Load %. That's because even with the engine on, you are running the fans and depending on your setting, the electric compressor may need to run for dehumidification mode. Also even though the car makes very efficient decision where to get the heat, sometimes the engine is not warm enough to generate enough heat needed for your climate setting. If that happens the car will still use the heat-pump for the instant heat generation until the engine comes up to the temperature needed. That being said, using the engine to warm the cabin will lower the AC Load % compared to using simply heat pump only, but of course with a lower mpg (more gas used).

 

In cold weather with the heat on, the car will run the engine more than it otherwise needs to, to generate heat. That reduces efficiency.

Also, the algorithm that calculates the climate score is very primitive. It seems to be mostly based on the difference in temperature between what the inside is at now, and what the setpoint is. It might also have preconceived notions about what is an appropriate interior temperature, based if it's hot or cold outside. It doesn't change in the summer whether or not the AC is on (which is extremely dumb), but it does seem to be higher if the engine is the primary source of heat than if the heat pump is on.

If you have the defroster on (defrost or feet+windshield), the climate score goes away (no bars) because keeping the windshield clear is the first priority.

I usually ignore the climate and eco scores. They just aren't very useful.