After evaluating several SQL and NoSQL services I ended up using Planetscale for my chrome extension Autotype[1]. I have a single db with tables to store user accounts, rich text shortcuts, role based access controls etc. I use Cloudflare workers and Planetscale's serverless library to interact with the db. The pricing is reasonable and the developer experience is great for an indie hacker like me.
My extension? It doesn't do any parsing, just stores whatever content is saved securely in the db. But you shouldn't ever save any sensitive data like this though.
[1] https://chrome.google.com/webstore/detail/autotype-free-text...