AudioSwitcher 4+

Seems to work well for what it does, but what it DOESN'T do is the problem.
I need to be able to switch the output between internal speakers and headphones while leaving my headphones connected. Apparently this is not actually possible without additional hardware.
Oh well, at least this app was fairly inexpensive.

Using Big Sur.

From the description it seems you can set priorities to different devices, so my—maybe naive—assumption was that input and output would be set based on the priorities assigned to whatever device was attached. Not so.

I set my bluetooth headset to priority 2, USB speakers to 1, and laptop speakers to 0. Switch Input and Output Device is enabled, and Only On Startup disabled. So I expected it to switch output to my headset when it's connected, otherwise to USB speakers when the laptop is docked, and if not, use the in-built speakers. None of this happens when I turn the bluetooth headset on and off. It just stays on what was set in the Sound control panel. Same for input devices.

I give it a couple of stars because there's a half-baked option to set up Device Profiles. So I set one to Bluetooth headset for in and output, and the second one to laptop mic and USB speakers. Well, it took me a while just to find out how to switch profiles. The only option I finally discovered was hidden on the Application Preferences panel and allows you to assign a hotkey to a profile. Why this is not on the Profiles page, is beyond me. It works, but why not simply add a popup to the menu bar item (maybe on a right click) to switch profiles. Remembering different keyboard shortcuts for different apps gets old very quickly. And why only two profiles? All in all, not impressed, even for just a couple of bucks.

I tried this app on a 14" M1 Pro MacBook Pro, and the only functionality I could get to work is the switching of the audio outputs. I couldn't get the audio inputs switched with a shortcut. At times, the shortcuts would stop working, and the app needed to be restarted. I could mute all sources with an app shortcut, but so I can do with the standard Apple mute button on the keyboard. I couldn't mute the mics with this app (even though the feature is there). Instead, when I would use Mic Drop to mute the mic, this app would show that the mic is muted (even on the menu bar), but this app couldn't exectute a shortcut set up within the app to mute the mic. All in all, this app is buggy and doesn't work properly. I want my money bac (yeah, good luck with that!).