Make sure your iPhone and the Mac running StageCom Control are on the exact same Wi-Fi network (not a guest network), and that the Mac's server is running (the StageCom Control window should show "ON AIR" or "STOPPED," not blank). If it still doesn't appear after a few seconds, try "Search again," or type the Mac's IP address directly — StageCom Control shows it in its console.
Go to Settings → Privacy & Security → Local Network on your iPhone, and make sure StageCom is turned on. You may need to relaunch the app afterward.
Make sure you're connected and live on a show first — the AirPods click only works while you're in a live session. If it still doesn't respond, disconnect and reconnect your AirPods and try again.
StageCom Control keeps your Mac awake automatically while the server is running. If it still sleeps, check Settings → Lock Screen isn't set to an aggressive display-sleep timer that overrides app-level wake assertions.