Your MBP 16" uses
USI BT and not Broadcom. I don't believe any of the latest M1/M2 Macs still use Broadcom.
Searching the internet a few people say these
https://www.orico.cc/us/product/detail/4103.html will work with Ventura 13.1 using just the Bluetoolfixup kext. If you want to try that, they don't cost much. SIP has to be disabled for the kext to load so do that as well. I can't verify that it will work as I've never owned one. Probably worth a shot if you are in a BT dilemma.
Newegg has them.
https://www.newegg.com/p/1GK-0001-00014?
Here's one more thing that might be important, a terminal command.
Option 1. Commands via Terminal
You can send a special command to the system through the terminal (command line), which will allow the system to use the Bluetooth Dongle by default for Bluetooth devices.
Enter the following command in the Terminal window:
Code:
sudo nvram bluetoothHostControllerSwitchBehavior=always
Then you'll need to enter the password from your Mac account and press Enter.