Kevin,
It may be I don't understand things very well and terrible state of ExtensionKit documentation doesn't help my case, but I don't think your proposal will work. I actually tried it and it didn't work, but like said, I'm not sure if I did everything right.
First of all, EXAppExtensionBrowserViewController is part of ExtensionKit, wheres FinderSync extensions have nothing to do (at least on the highest level) with that framework.
Secondly, as I understand it (and I'm not sure about it and again, terrible state of documentation doesn't help), EXAppExtensionBrowserViewController is supposed to be used to list and enable/disable extensions hosted/embedded in OTHER applications, which has NSExtensionPointIdentifier matching custom extension points declared by OUR application.
But here, we actually have problem with OUR application, which is a host/container of FinderSync extension, with NSExtensionPointIdentifier = com.apple.FinderSync. It is the responsibility of some OTHER application (defining com.apple.FinderSync extension point) to provide user interface to list and enable/disable FinderSync extensions. And that has being done by System Preferences / System Settings application, until Sequoia.
What I did:
I left my application, hosting a FinderSync extension, just as it is, but tried to show EXAppExtensionBrowserViewController. I got an "empty" window, just saying "Select extensions for customizing FIleUtils:" (FileUtils is my application name), without any following list of extensions (and applications hosting them).
I even tried something crazy, trying to declare my "custom" extension point com.apple.FinderSync in the .appextensionpoint plist file (copied during build phase into ExtensionKit Extensions destination) and then show EXAppExtensionBrowserViewController. The result was the same; "empty" window, just saying "Select extensions for customizing FIleUtils:", without any following list.
And we actually need a window, which would say Select extensions for customizing Finder:, since that's the application (declaring extension points) which our FinderSync extension (bundled into our application) wants to customize. And for that purpose we have +[FIFinderSyncController showExtensionManagementInterface], which worked fine before Sequoia.
Please let me know if I should do something similar to enable FinderSync extension using EXAppExtensionBrowserViewController. But as far as I understand how ExtensionKit works, that's not the way to go.