eve This problem just started happening to me again after upgrading from Cheogram 2.15.3.2+free to the same version you mentioned. Unfortunately at the same time I also upgraded to the latest GrapheneOS 2024111800 (on a Pixel 7) so I don't know which upgrade caused the problem. It took almost a week before the problem appeared.
There are a few differences this time. When calling from the phone dialer (after integration) there is rapid flashing of the speaker/bluetooth icon as it switches between audio output. This now happens consistently where before it was infrequently one of the several different symptoms. When the call connects it again changes to the phone speaker instead of my connected BT headphones, as before. This time it seems I can keep the android integration set and still use the app directly and receive calls with no problem (at least so far).
I tried briefly to look into downgrading Cheogram to my original version but couldn't easily figure out how. Unfortunately I don't have time in the near future to troubleshoot downgrades and deal with possible side effects.