"Algebraic Effects" is sort of a misnomer.

It's the name given to a specific idea being (re)explored in programming languages. Basically it's a try-catch except when you catch the error, you can do something, then return to where the exception was thrown and continue from there.

The second half of the article is similar to the idea of Algebraic Effects.

Here's another article explaining Algebraic Effects: https://overreacted.io/algebraic-effects-for-the-rest-of-us/