Hi @Marcus Fugett ,
1)If you want to hide the sync button in SharePoint library:
Go to Library Settings> Advanced Settings> Scroll down to the middle of the page, and under Offline Client Availability, select No (default is Yes)> Click OK at the bottom:
You will now notice that the library lacks a Sync Button:
2)If you want to disable sync at the Site level, please go to Site information> View all site settings> Click on Search and offline availability under Search:
Under Offline Client Availability select No:
Now you will see the Sync button disappear from all libraries located on this site.
More information for your reference:
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