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That sounds like a job for a browser extension... A quick search comes up with Anki Quick Adder [0] for Chrome, but nothing equivalent for Firefox.

[0] https://chrome.google.com/webstore/detail/anki-quick-adder/g...

As someone who suffers from the same problem, something like SuperMemo may be a close enough solution. I've never used it myself, but I know it has features such as "incremental reading" where you add pages to the database and mark pieces of it to read a little at a time.

Check out https://withorbit.com - an ongoing research project (and set of tools on github) to embed SRS into any essay/post. If more people adopted it, you might have what you want.