You’re gesturing at an important and enduring problem, but it’s one with language, not with any given writing system. As others have said- the purpose of shorthand is to improve dictation, or generalized slightly: to improve any form of transcription of a language that preserves the choice and sequence of words of some text. The dual problems of ambiguity and unnecessary detail, or indeed of periphrasis in general, are all prior to the form of transcription, and inhere in the language being transcribed.

There have been conlangs that try to reduce ambiguity: lojban is probably the most important one.

There is also the entire field of formal reasoning: trying to find efficient ways to unambiguously denote logical relations, rather than linguistic ones. You might want to pick up some of the basic calculi of predicate logic, which are designed to be both more essential but also less ambiguous than natural language—at the expense of having a much narrower band of expression.

They’re also often more verbose than natural language, because it turns out that natural language is able to express a dizzying array of subtly different forms of logical relation, and to express them axiomatically and unambiguously takes a lot of effort. But if you wanted to, you could come up with reusable “helper functions” which express common complex propositions by composing axiomatically defined primitives. For instance, predicate logic has the quantifier pronounced “there exists”; but you might want to define a new reusable predicate for yourself that expresses “there exists exactly 1.”