Hi LizRC,
Welcome to the Apple Community. Thank you for posting your question.
Re: microphone icon... "can’t get it to disappear"
Seems one of the apps below is in use.
The microphone icon means that your Apple Watch mic is listening.
It appears when you're talking to Siri,
recording a voice memo,
or using any app that activates the microphone,
such as Handwashing or Walkie-Talkie.
above info. is from Apple Support's article: Status icons and symbols on Apple Watch - Apple Support
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Re: "It seems to be draining my battery"
You might want to ensure that audio is not being recorded in the background ... that would really use a lot of power
else ... one or other of the above listed apps may still be actively in use.
All the best :-)