Increment Filename until Unique

In the File Browsers context menu:

add a method of increasing a filename until it is unique. Either as another argument to the existing bpy.ops.file.filenum(...) operator OR as its own operator.

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Add a keybind:

clicking the increment number icon (+) in the file browser while holding SHIFT should increment the filename until it is no longer overwriting another file, aka, unique.

Mockups:

Increase until unique button (video):

How it works currently:

How it should work when holding SHIFT: