There are several ways to approach this question. But first we need to question the very concept of monosemy vs. polysemy. They are a stretch even when it comes to the lexicon let alone very abstract constructions such as 'perfect' in English. What would that single meaning even look like? How would be multiple senses related distinct? How is it represented in the competence of native speakers? How do non-native learners acquire a similar competence and how do they represent the perfect meaning?
When you approach the meaning of the perfect (as opposed to the present, past and future perfects) you could approach it 1. from a logical perspective on time, action, sequence and completion or 2. from a functional perspective dealing with things like experience, knowledge, perspective. You will also need to deal with modality.
To deal with the perfect on its own, we first need to find its usage and this will obviously be embedded in the context of tense, modality and communicative function. However, the question is, when all else is stripped away, are we left with some distinct, single aspectual meaning (like completion) that is the perfect's unique contribution to every case of use.
My go to approach here is Lakoff's (and others') treatment of things like 'over' and the existential 'there' construction. He showed that they have several related semantic cores (a case of radial categories) which motivate but do not straightforwardly predict their various uses. (While people have found fault with details of the analysis, the key point still stands).
I suspect that a careful analysis of the 'perfect' would arrive at a similar conclusion. There are several related highly abstract meanings related to experience, completion and even sequence that motivate its meanings in all (or most) of the various contexts of its use but that any individual use cannot be predicted by them because of the influence of all the context.