Sometimes stuttering bluetooth connection on car radio

My issue is not a big issue, but a bit tedious. My car has no android auto. But the entertaining system supports bluetooth audio, phone, maybe others. When i use my Fairphone 6 to play audible audio books. It starts well, with no issues. But sometime, if an audio notification from a sms or whatsapp comes in, the audio books stutters for some seconds. Also it does not stop playing if i switch to radio. With my previous phone (an older xiaomi mi 10 lite 5g) this all was not happening. As i said, its not a big issue, but i would be glad to know, if there is a way to improve the connection.

My car is an older Audi A4 Avant without Android Auto, where i cannot update anything.