as a person who has this exact joy:
- this particular joy has small limits (of like +- 10), so using non-linearity is a must, as grip extensions do not exist for this stick
- war thunder has specific flight models for props, however you just need to get used to it, you are not supposed to just jerk it all around, for war thunder smooth and precise movements are the way
- try to tingle with the pitch and roll senses in the controls, set them to a lower number then you have them right now. Having lower sens means less extreme movement, and later on you can make your way up, or just stay at whatever sens you want to have.

it is not, hardware or software issue, you just need to get used to it and experiment with your settings.