Not sure if this will help, but for me I was able to permanently disable the handsfree part of my bluetooth headphones by disabling the system device entry for it in the Device Manager->System Devices area on my Windows 11 machine. (Note that the system device is different from the driver and represented by a different icon (for me a computer tower and blue pane monitor):

Simply right-click and disable:

I have noticed that this method requires me to have to hit the connect button in Bluetooth & devices -> Devices more often / almost every time I turn my headphones back on, but it has helped me not have to disable the handsfree device every time which I found just a bit more cumbersome. Teams also now picks up the proper device so I don't lose audio.
SOLVED !!!!
NOTE: This will only show under "System Devices" (as pictured) IF you have the headphones connected AND have NOT unchecked handsfree telephony in [ Devices and Printers > Headphone Properties > Services ]
I have been dealing with this for YEARS and THIS IS THE ONLY PERMANENT SOLUTION I have found. Not to mention it is SO easy.
Before this solution, I had a link on my desktop to "Devices and Printers" and had to uncheck "Handsfree Telephony" every time my computer booted for my headphones to work normally while gaming and using discord.
I use Bose Quiet Comfort 35 Wireless Headphone II
So, once again for the search algorithms:
HOW TO PERMANENTLY DISABLE HANDSFREE TELEPHONY ON WINDOWS 11 FOR BOSE QUIETCOMFORT 35 WIRELESS HEADPHONE II FOR PERFECT AUDIO QUALITY WHILE GAMING AND USING DISCORD.
HUGE thanks to @ElectricDrake