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Dear Jonathan,
Do you need further help?
Your requirement is easy to be achieved by PowerApps.
Here is a demo for your reference.
As an example, I create three libraries for Department1, Department2 and Department3. You can create a collection naming departmentcollection in PowerApps.
Connect the three libraries to PowerApps and insert a table control.
Add a button Create Index Collection to update the libraries' files in PowerApps.
Type Remove(departmentcollection,departmentcollection);ClearCollect(departmentcollection,Department1,Department2,Department3) on OnSelect.
As the Department column is Choice type, type ThisItem.Department.Value on the column text.
Add a text input control as the search box. The xontrol in my environment is TextInput1.
Type Search(departmentcollection,TextInput1.Text,'File name with extension') on Items on the table control as the search resource.
Finally add a button Go to selected item for users to open the file when they select the result file from the table.
Type Launch(DataTable1.Selected.'Link to item') on OnSelect.
Now publish the app and embed it on a site page in SharePoint Online for users to search the files.
Use the Power Apps web part - Microsoft Support
Result:
Welcome to share any update at your convenience.
Your efforts and time are greatly appreciated!
Sincerely
Cliff | Microsoft Community Moderator