If you want to use the auto-update for Event Gallery Extended, you need to configure the DownloadID at the components options with this value:
Please log in to see your DownloadID.
In Joomla4, you manage the download id in System -> Update Sites. Usually, after installing Event Gallery, you can follow the process described in the images below.
In Event Gallery, you can enter the DownloadID in the components options like that: