Edited 3/15/24.
See this Beta announcement for developments on caption/text styles:
https://community.adobe.com/t5/premiere-pro-beta-discussions/now-in-beta-premiere-pro-text-styles-en...
Original post:
Currently, to share a Caption Track Style, it must be saved to disk from the Project Panel, then imported to a new project. Several users are asking for an easier way to share across projects and with their team members. In the Beta forum, staff indicated in Dec 2020 that "loading from libraries" was part of future plans. This is needed.