Ok, so the devs patched it for sure this week (did something). But some folks are still having issues. I think we've finally figured out at least some of the tricks to make it work - so popping it all in here for everyone :
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Make sure in Windows 10 Privacy Settings that both the Xbox App and Sea of Thieves are allowed to use your Mic.
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In the Xbox App - Go to the GEAR - and make sure to select your microphone that you want to use. Have to have it.
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Next In your Sound settings (right click your sound on your taskbar and go to Recording Properties) - Select your mic and you want to do THREE THINGS : 1) Make your mic the default device. 2) Make it the default COMMUNICATION DEVICE (Very important...we just learned this is HUGELY used in this game). 3) make sure to go to properties on your mic and put your level all the way up.
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Now, In game - Make sure you have Push to Talk checkmarked, you have chat to 100, and Directional set. Additionally check your default button, change it to something else for the heck of it.
At this point it SHOULD be working for you, so long as something else funky is not up with the code. Always be sure to test with an Xbox Party Chat to make sure they hear you fine as well after doing all of the above.
Hope this helps.