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Updated Dec 07, 2020
Version 2.0
Blog Post
We now know there's no way to disable "Add Shortcut," which would be fine aside from the fact that there may be no way to disable the "Sync" button....
Update: After seeing posts that the above-mentioned Powershell to hide Add Shortcut was still working, at least if you have a current SharePoint Online Management Shell (I tested the one from early June 2021), I can confirm that it does still work, though what it says when you implement it makes me wonder for how long: "WARNING: Users in your organization will no longer be able to add new shortcuts to their OneDrive while the feature is in Public Preview. However, existing shortcuts will remain functional."
And for those wanting to do the opposite, meaning keep Add Shortcut and hide Sync, there's a way to do that, too, apparently very new since I had to notice it myself in Get-SPOTenant:
Set-SPOTenant -HideSyncButtonOnTeamSite $true
WARNING: Users in your organization will no longer be able to use the "Sync" button to sync TeamSite content. However, existing synced content will remain functional, and users can still sync content via their OneDrive using the Add shortcut command.