I found that there were three things I had to adjust to get snipping tool to record from the microphone:
1 - I had an music player (foobar2000) running in the background, idle. To avoid conflict, I closed this program.
2 - My Microsoft Teams was configured, under Devices, to use the my bluetooth headset as both the speaker and the microphone. After I configured Teams to use other devices, I no longer received the error 'If an app is using WASAPI exclusive mode, change it shared mode.' (fyi, nice grammer...)
3 - In the Sound app in Control panel, I had disabled Stereo Mix as a recording source. Since there was nothing else available, I had to re-enable this input so that I could accomplish #2 above. Otherwise, Teams only allowed me to choose the headset as my microphone.
Prior to that, I had restarted the Windows Audio Endpoint Builder service which is all you need to do. Due to dependencies, this also restarts the Windows Audio Service. But that had no effect.
After recording from the microphone started working, I tried to change all the settings back to see if the problem reappeared--it did not. So, I'm not sure the precise thing which resolved the issue--I'm hoping these steps will give others ideas on how to overcome their recording issues.