Now, there is a huge nuance here, which is that you are moving near the speed of light, to certain observers. This is like the whole "relativ-" prefix in "relativity", you are at rest in your rest frame, you are moving very fast in some other rest frames. The cosmic muon crashing into Earth, sees you as time-dilated! So with that nuance "we experience time at nearly the speed of light" just becomes kind of a tautology like "we experience time how we experience time."
But a better way to think about this is, you are about two meters high, you are about a meter wide, about a half-meter dorsoventrally... and about 30 000 000 m in the other direction, if we're looking at the human reaction time/blink-of-an-eye range of 0.1s (think about how 10fps video is at the cusp of being continuous and how 20Hz is where clicks stop sounding differentiated and instead start sounding like a bass note).
What this means is that if we look at you relativistically, you kind of look like a big "rope" with worldlines of other atoms coming in, braiding into your body, eventually leaving... but the strands of this rope are bundled into these cells that have worldlines over 99.9999% parallel. (Atoms within those cells move faster, but you're probably at least 99.999% parallel even if we make that statement?) And that astonishing parallelism is precisely why relativity is not very intuitively plausible to us.
So: distance over time, but is the time dimension only measurable in distance over time? Is there a purely time unit, or does that not make sense when speaking of spacetime?
But ratber it's that there exists an operation which is almost entirely like rotation, but it rotates x, y, or z into w=ct, where w is measured in meters just like x,y,z are, but t is measured in time units, and c is the speed of light converting between them. Instead of a rotation's formula with sines and cosines like
x' = x cos θ + y sin θ
y' = y cos θ – x sin θ
(x')² + (y')² = x² + y²
w' = w cosh φ — x sinh φ
x' = x cosh φ — w sinh φ
(w')² – (x')² = w² – x².
The fact that you are discretely "you" about ten times per second, I am taking as a fact of biology. But if you try to convert that biology into physics, that's where you convert t into w to get that t=0.1s converts to w = 30,000 km.