Over the last decade or so, Apple has been moving steadily toward fewer and more complex field-replaceable components. This reduces the total cost of parts floating about in inventory, not earning their keep.
The field-replaceable sub-assembly for a 14-in display flex cable issue is the display assembly, complete. That runs around US$500 for the Apple repair with a modest warranty.
This is no longer a simple repair nor a cheap one, and is unlikely to be performed while you wait. Typical in-store turn around is about three days, PROVIDED parts have been reserved and are on hand.
Your can also consider a mail in repair as an alternative, but that can be about ten days start to finish, again depending on parts availability. (but more likely to actually have parts on hand at a regional depot than an individual store.)
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If there were a third party way to replace just the surface-mounted flex cables, that was reliable enough to do on customer's equipment on demand, we would have heard about it here. Alas, there are not even rumors of such aftermarket repairs.