tldr quick resolution - in the schematic right click the part and select "Replace"

NOTE: You should probably go into Library Manager and disable the old library (if it's present on your system) so that the list of replacement parts will point to the correct library - this becomes an issue for those of us with really complex historical designs that started on Eagle Desktop, used library.io and then have migrated to the official Fusion Team Library method - if you are like me you'll want to make sure to look carefully during part replacement to be sure you are pulling the 'new' version of the part from the correct source.
-- note about the underlying mechanics --
Fusion uses a sandboxed copy of EagleCAD under the hood, so the data model (at least for now) still looks like the good old days - once you place a part into a schematic the Eagle SCH file that does exist (but is carefully hidden on your filesystem as a temporary file) contains a full copy of the data that was in the source Library and a URI of some sort connecting to the source - that URI is used when you select "Update Design From Library" to synchronize changes in the Library source to your SCH/BRD file in the active editor. Because of this legacy data model, its possible to have parts in a schematic for which the original library is no longer accessible, or is significantly different (symbol, footprint, attributes, etc.) so WATCH OUT FOR DRAGONS...