I think the bottom line here is that Time is not a "dimension" in any sense that the spacial dimensions are. However, we humans have found it "convenient" to consider Time as a pseudo-dimension, using various assumptions and math tricks in order to get the units to come out right and the geometry to come out right. With our shiny new "Space-Time Coordinate Systems" we can accomplish some pretty fantastic Science, and have massively increased our understanding of the Universe and Reality.
But we must not forget that the "Space-Time Coordinate Systems" we have constructed, are indeed, constructs. They do not "exist" in the same way that atoms and photons exist.
From our constructs, we obtain a facility with calculating Time, measuring Time, interpreting the effects of Time on matter and energy, interpreting the effects of matter and energy on Time --- BUT...
These constructs do NOT tell us what TIME ITSELF IS
Time is non-material, non-energy, non-positional and non-"thingish". We have no power to access it or control it. It has no constituent parts, no texture, no measureable "substance" of any kind. It has no boundaries so that we can identify Time against a background of Not-Time. It is an invisible ghost that is always everywhere and never still.
Okay, so what is Time? I dunno.
For the time being, it is a concept
, a fabrication of mental/semantic structures and mathematical models.
And yet, Time would STILL be one of the core, foundational "attributes" of our Universe and Reality itself, even if we
did not exist. There is this "attribute" that EXISTS independently of us and our understanding.
And "Time" is the name that we give -- NOT to the "attribute" itself, but to our experience
of it. "Time" is the name we give to our experience of having "memories" of events and things and images that no longer exist.