Could you check whether the update to iOS 16.1 helps?

And I can see the situation when resetting iPhone fixes this behaviour but only like for 2-3 new BLE connections. Then again DLE is broken.

1 here, the same thing happened to our project. After updating to iOS 16+ the negotiated DLE size dropped from 251 to 170 and MTU from 244 to 20. Could anyone do anything about this? Is there any chance to handle this on our side ?