For me, your game also plays sound immediately, without the need for any special clicks. Although the audio context is initially suspended (log shows Web Audio context is suspended....) but then it just plays immediately. Something / somehow must resume the audio context in your case magically:)
Maybe the <iframe with allow=autoplay... (I understand this is standard wrapper by itch.io) does the trick?
I’m testing this in FireFox, same browser where e.g. my example platformer requires a click before music is heard.
I guess, kudos to itch.io for wrapping games in HTML that makes it “just work” 