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You cannot export the component Options (at least not in any straightforward manner), but you can definitely export backup profiles and import them into a new installation. 

Go into Akeeba Backup, Profiles Management. There's an Export button next to each profile. It lets you save it into a JSON file.

On the new site, install Akeeba Backup, go into Akeeba Backup, Profile Management and click on Import in the toolbar. You can now upload and import those JSON files.

Caveat: You cannot import into profile #1 (the default backup profile), nor can you delete it. Rename it as "DO NOT USE" or something similar.

Caveat 2: You cannot import into a specific profile number. Profile numbers are created sequentially when you create or import backup profiles.

This feature works great! I am using it to sync backup profiles for specific test cases across my Windows and Linux development machines, and also across Joomla 4 and 5 development sites (setting up things like Dropbox, Amazon S3 etc from scratch is a pain in the posterior if you need to do it several times a day).

You're welcome!