There is, the damn spacetime, under all it's completely tangled together, you can't separate them, because relativity. It's a very useful "illusion" for everyday life, to think of time as something completely distinct and always present... but it seems, our best experiments and thus models suggest otherwise. Similarly with quantum stuff, there doesn't seem to be hidden variables, it's truly a probability distribution.

Thanks in this case I am trying to understand what is meant by “moving through spacetime”

> what is meant by “moving through spacetime”

AIUI the equations describe a path through spacetime. There is no "speed" or "movement" along this path, or at least none with an actual physical interpretation. The path simply has a certain shape. The equations define the path as a parametric function, and you could in principle calculate the change in 4D spacetime coordinates with respect to the change in that parameter, but it would have no physical meaning. To keep things simple, in a canonical representation of the path this ratio (the "speed" through spacetime with respect to the arbitrary scalar parameter—though "speed" is not really the right term since the parameter does not represent time) is held constant and defined as the speed of light.

To put things in more familiar (or at least less spacetime-y) terms, these very different parametric equations both describe a 2D unit circle with respect to an arbitrary parameter r with range (-∞, ∞):

    p(r) = [cos(r), sin(r)]
    q(r) = [abs(2 - t) - 1, ((2 - t) / abs(2 - t)) * sqrt(1 - (abs(2 - t) - 1)**2)]

The "speed" of p(r) with respect to r is the magnitude of the derivative [-sin(r), cos(r)], a unit vector, and thus equal to one for any value of r. The magnitude of the derivative of q(r) is something rather more complicated, and not even well-defined for most values of r. However, they both describe the same circle. The parameter r is not part of the path; only the set of [x, y] coordinates counts, and p(r) and q(r) describe the same sets of 2D points.

Sitting at home, orbiting a star, falling into a blackhole, or being a photon, an electron, or a GPS sat. All are moving through spacetime, of course on different trajectories.

Especially when looking at them with the lens of General Relativity.

There is, it's called the "spacetime interval". It's relative to the observer, because everything in spacetime is, but it's the "true" measure of separation in spacetime.