Google will close down Picasa Web in May 2016. This is bad for all Event Gallery users which connected Picasa albums so far. But there is hope. Unlike the web frontend and the Picasa desktop application there is no word that the Picasa Web Albums Data API will close down. Instead there is a message which tells us that there will be some changes to this API published in March 2016 (Picasa Web Albums Data API Website):

Important: Beginning May 1st, 2016, we’ll start rolling out changes to the Picasa Web Albums Data API and no longer support the following functionality:
  • Flash support
  • Community search
  • Mutation operations other than uploads
  • All support for tags, comments, and contacts
The API will still support other functions, including reading photos, reading albums, reading photos in albums, and uploading new photos. Although these operations will continue to be supported and the protocol will remain the same, the content included in the responses and the operation behavior may change. We'll update the documentation on this site with specifics on the changes in March. Read other important Picasa updates here.

Based in this I hope that we can continue using the images you upload the Google Photos on your Joomla! site. Since currently can't derive the necessary connection data from the Google Photos URLs I assume that the API-update helps with that. For now this page can help you getting the userid and the albumid: Event Gallery - Picasa Album Selector. This selector is build into Event Gallery 3.5.

For the worst case scenario there is already a kind of workaround. Event Gallery 3.5 supports Flickr. If you're short on local storage you can migrate your images to Flickr as public imageset and connect them to Event Gallery.