Notifications on MacBook affect iPhone that are listening with bluetooth headphones

Looks like there is a fair amount of issues with this over the years, but what I'm getting is a little different. This is really annoying when listening through Spotify because the song stops, but also the dings from various Mac apps can get really loud.

Status:

Listen through iPhone (2nd gen SE) speakers alone and MacBook (Air, M1, Ventura) notification comes in: Fine.

The notification pops up or makes a noise on the MacBook as the settings are set.

Listen to the iPhone through Bluetooth and the MacBook is out of range or off: All good.

Playing music on iPhone through Bluetooth and MacBook notification comes in: Bad.

Spotify stops songs. Loud dings and beeps from the Mac are heard in earphones. However banners don't show on the phone, only the Mac.

As far as I can tell this is because if I look in the MacBook bluetooth settings, I see that powering up the headphones has double connected to both the phone and the MacBook. I didn't ask for this, and can't figure out how to stop it.

On the MacBook, I can disconnect the headphones from bluetooth which temporarily fixes the problem...MacBook beeps and notifications stop getting shared with the iPhone. But the next time the headphone has the opportunity to pair with the MacBook, it does, and the problem starts again. Or I could turn off bluetooth on the Mac, which has other disadvantages.

I can sort of fix it by forgetting the headphones on the MacBook bluetooth settings. However, I do sometimes want to listen to my MacBook through bluetooth to the headphones, so I'd have to always do that and then re-pair the headphones each time.

Apparently Apple's listening devices don't have this problem according to: https://www.reddit.com/r/MacOS/comments/ql60cm/how_to_disable_automatic_bluetooth_connection_to/

There is an option for those on the Mac to autoconnect "when last connected to this mac" which would seem to solve it.

Is there any other solution available? (Both my iPhone and Mac are under Applecare, but I'm afraid using support would probably not be productive—as I've already gone through a bunch of troubleshooting and reading.)