If someone wants to comment on your blog, they can write their own blog post on their blog and send a webmention. That can get linked at the bottom of your blog post with a text snippet summary.
There's no "API" beyond "curl -i -d source=URL -d target=URL WEBMENTION_ENDPOINT" in the traditional sense. Using microformats markup for better exraction is optional.
The result is a federated system of comments owned and controlled by nobody except the original author. No need to use someone's Matrix server or spin up your own. It also imposes a bit of a barrier to entry (must have your own (micro)blog), but if you don't want any random person to leave a comment that can be a feature.
Services like brid.gy turn Fediverse and Twitter comments into Webmentions as well; I've thought about using it for Fediverse comments in the past, but I don't want to host a new program or rely on a third-party service.