I suspect that a reasonable WordPress user could probably set up a free Hypothes.is account and use the RSS feed from it (something like https://hypothes.is/stream.atom?user=username) to create an IFTTT.com recipe to post it as a public/draft to their WordPress website.
My version presented here has also been augmented by also using the Post Kinds Plugin to which I’ve manually added a custom annotation post type along with some CSS for the yellow highlight effect. These additional coding flourishes aren’t absolutely necessary for those who just want to own the data on their website.
If you want to get even fancier you could also do RSS to IFTTT to do a webhook post to an Micropub endpoint or custom code your own solution using their API. Lots of options are available, the most difficult part may be knowing that something like this could even be done.
Chris. Do you have any step-by-step instructions for the specific workflow?
Syndicated copies:
On my site (naturally). Try:
* https://boffosocko.com/2020/05/30/hypothes-is-annotations-to-wordpress-via-rss/
* https://boffosocko.com/2020/01/21/using-ifttt-to-syndicate-pesos-content-from-social-services-to-wordpress-using-micropub/
* https://boffosocko.com/2018/06/23/an-outline-for-using-hypothesis-for-owning-your-annotations-and-highlights/ (somewhat related, and possibly useful for your Obsidian work?)
Syndicated copies:
The Lightning Introductions and Website Demos is where notes from this session at IndieWebCamp 2020 West can be found.