How far should I develop the main ideas in my paper before publishing it?
One idea per paper, from my experience on AI and related formal work. Implications are typically left for the last part of the conclusions. Look at a typical paper in the area you want to publish in and see how far they go with those implications.

You can write a separate (mathematical) paper on implications across areas. It is not unusual to publish concerning the same idea in multiple fields. This - could be - salami slicing but it can also be extremely useful to practitioners in those fields.

For example, the seminal paper "On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games" by Dung took formal argumentation, gave it an abstract graph-theoretic conceptualisation and semantics, and then showed morphisms between previously separate areas.

If the implications you look into would change the title of your paper or the introduction to include words such as "role" or "link" or "morphism" then that may be a different paper.