How to sync my transcript I edited to captions

Unfortunately they don't "sync" per se. Once the captions are made they are separate from the transcript. You either need to manually update the captions to match the new edits in the transcript OR simply wait until you are certain the transcript is correct before creating captions.

For now, you can delete the caption track and quickly remake them based on the updated transcript. If you've applied text styling you can save that as a STYLE in the Essential panel (before deleting them) and apply it to the new captions in the Style dropdown menu in that pop up window.