@JamesTheGray2
Swapping datasources on a control in PowerApps is usually not a good thing.
You can do this in a couple of ways:
1) Shape the data signature from each datasource to match a common set of columns that you NEED for your Gallery. For example, if you only are displaying 5 columns in your Gallery, and these are "common" between all of the libraries, then you can implement a Switch statement, but you need to switch between "Shaped" datasource - meaning that you need to use a ShowColumns function on your datasources to specify the exact same columns for each source that you want.
ex.
Switch(someCondition,
"conditionA",
ShowColumns(source1, "ID", "FineName", "Title", "Created"),
"conditionB",
ShowColumns(source2, "ID", "FineName", "Title", "Created"),
"conditionC",
ShowColumns(source3, "ID", "FineName", "Title", "Created"),
etc..
)
(You can also simplify that by just switching on the data source, but you get the point).
2) Provide a Gallery for each list in your App. Then use a switch statement on the visible property of the Gallery to only display the one you want for that team/user.
Keep in mind...(for #1) if you want to implement an EditForm for any reason, do not use the .Selected of the Gallery as the signature of the record will not match. You will need to lookup the record. BUT...there is no such workaround for Forms in regard to the DataSource. So you would need a form for each library - again, if you need such functionality.
I hope this is helpful for you.