Notification sounds being suppressed

I work in the gig economy, so a large chunk of my income depends on me being able to react quickly when a job offer comes in. Unfortunately, Android Auto is interfering with this: when I'm not connected to Android Auto, my phone chirps at me whenever an order comes in; and if I deem it safe to do so, I can immediately check to see if I want to accept the order. With Android Auto, that audible chirp is suppressed. As a result, I have to keep an eagle eye on my phone to avoid missing jobs while I'm driving. This largely defeats the purpose of suppressing the notification sound.

So how can I bypass the suppression of the gig app's notification sound?

That toggle is already off.

After some further troubleshooting, it appears like this may not be an Android Auto problem after all; it may be a Bluetooth issue: the notification sound is being suppressed when I'm in my car and the Bluetooth has taken over handling such things as phone calls and playing audio streams, but before I've physically connected my phone to the car radio and brought Android Auto into the mix.

So maybe what I need is something that keeps some or all of the phone's Notification sounds from being rerouted through Bluetooth, which appears to not be doing anything with them after receiving them.