I can’t conveniently test this right now, and I’m still using Mojave – so that might interfere as well.
Nevertheless – here’s how I’d start working with this:
activate application "FaceTime"
# Make sure there's not a timing issue here.
tell application "System Events"
tell application process "FaceTime"
tell its window 1
tell (first button whose accessibility description is "mute")
return actions -- check the available actions
# Then probably
# perform action "AXPress"
end tell
end tell
end tell
end tell