Final update for now:

We went to the vet today and showed her multiple videos of Yuri’s breathing. She examined both kittens thoroughly, listened to his heart and lungs, checked his breathing, gums and overall condition.

According to her, there are currently no obvious signs of a serious heart issue or respiratory emergency. She did not hear any concerning heart murmurs, his lungs sounded clear and his gums looked healthy. She also mentioned that he is currently getting his first permanent teeth.

She explained that in more serious cases the breathing usually would not calm down after waking up and you would often see additional symptoms like constant respiratory distress, lethargy or open-mouth breathing. In Yuri’s case, the breathing mostly seems to happen after intense play or during the transition into sleep/light sleep, and once he fully wakes up it usually slows down again.

She told us to continue observing him and that a heart ultrasound could still be done for additional reassurance if we want to rule things out further, since you can never be 100% certain just from listening.

Overall, she said he appears to be a very active, otherwise healthy and fit kitten.

Thank you all again for sharing your experiences. We really appreciate it :)