I'm not sure this falls within the scope of answers you're looking for, having tagged your question
science-based so maybe oriented more towards what we can model mathematically (though not all disciplines of science are about mathematical modelling). Anyway, with that out of the way:
Makes me think of the way God packed up the essence of himself in a tangible human person by the name of Jesus Christ.
I don't think I can cover even most important aspects here (and some may be well beyond the scope of your question proper) but I'll mention that we can observe here
- a person apparently fully out of this world, interacting and being interacted with by the people around quite normally (save the extras, come to that in the next point) and being perceived as one of them (even to the extent that some are adamant about that)
while as things develop, we see a meaningful number of the people, as they encounter that person, discovering that
- there's a lot more to that person than what's visible at first sight, and a connection with a reality that obviously goes way beyond what people are used to.
So we can go from here and make observations on what happens to, with, and from the person from the higher-dimension system and how it plays out to and in the lower-dimensional system.
It's interesting what possibilities this offers for interaction and how the interaction goes on here. For one, that connection with the higher-dimensional reality (to name it in terms of the question) is obviously not forced on the people around - as we see some bluntly ignoring it - while we can tell from the fact that we see others interpreting it to be of whatever nature and source they like to think of, that there is something going on that is hard to ignore without choosing so.
It can further be observed that the person immersing in the lesser-dimensional world is fully at liberty to reveal of his true nature as little or in fact as much as he chooses to, only limited by the degree to which the individual people are capable and willing to understand (or may be helped to understand by the person revealing).
Which in this case leads to an amazing and, in some dimensions (including what some would call metaphysical), even total extent of interaction with some who agree to it.
As for some other points of your question, there seems to be no falling into wormholes or similar involved here, rather a kind of total control of the overall reality including the parts of it that are perceivable in the lower-dimensional space - while most aspects of it are generally left untouched (and the same obviously goes for the freedom of the people around to be doing what they choose to, but that's outside the scope of your question).
So to add this angle, there is no falling into a wormhole of any elements of the lower-dimensional system either (albeit there is some access to aspects of the higher-dimensional system as provided by the person immersing).