It seems that hardcover has library data import but not export.
It makes complete sense to have a CSV export (and a CSV import!). Ideally the same format you can export to, you'd be able to import into Hardcover. That way someone who manages their own library in Excel or Google Sheets could make a few changes and import their library into Hardcover.
Marking this as "In progress" since we're currently planning out this format. Hoping to release both the import and export this year.