Wow, that is a major pain. I was totally unaware of Google going away with hosting. I found this article:
Host web pages with Google Drive - Drive Help
It seems like it's just for hosting web pages (which sucks since I use this), but, like you said, there is a process to changing the URL of the photo to make the photo sharing work. It looks like that how back-door-approach is going away. This sucks.
I see Google is trying to promote their new "domains" thing too: Google Domains – Google
Though, that still doesn't help the photo sharing thing.
Have you looked into the "new" Google Photos? Even so, from there, I cannot find an easy way to grab a web address that has a photo extension on the end of it (like .jpg and .png).
Here is an Esri blog on using Google Photos:
What story map authors need to know about the transition from Picasa to Google Photos | ArcGIS Blog