The audio output from the Streaming Stick is contained in the HDMI signal. You can buy an HDMI audio extractor that will pass the video through to your monitor, and provide a separate audio output that you can then connect to whatever audio system you wish.
Amazon HDMI Audio Extractor page: https://www.amazon.com/s?k=hdmi+audio+extractor+converter
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Streaming Stick 4K+ 3821 | Streaming Stick+ 3810 | TCL Roku TV 43S245/C107X