...isn't the front-end back-end split about dividing by purpose? Front-end is user interactions; back-end is about data retrieval and storage (some which might be the user interactions supplied by the front-end).

Ultimately either can do analysis of data, though tradeoffs generally push that to one side of the API or the other.

I guess, the question here is: How to group tech to one solution?

Take Auth0, for example they give you a full stack solution for the purpose "authentication".

But, yeah, the more low-level your purpose, the more technology specific a solution you will be.