Instead of attempting to build a Power App that dynamically switches between multiple data sources, I would recommend architecting the Power App to capture the picture and send it to Power Automate while passing necessary parameters about the construction site. Power Automate can then handle writing the picture to the appropriate SharePoint site.
In this approach, Power Apps would send the picture to Power Automate, providing the construction site info as a parameter. Power Automate can be configured to handle the logic of determining the correct SharePoint site and list for the upload, based on a mapping list that stores the relationship. This way, there's no need to bind numerous data sources directly within Power Apps, avoiding potential performance issues associated with a large number of concurrent data connections.
For more details on optimizing performance in Power Apps and managing data connections effectively, you can refer to the Microsoft documentation on performance tips.
If I have answered your question, please mark your post as Solved.
If you like my response, please give it a Thumbs Up.
Cheers!
Rick Hurt