What did Minkowski mean by his statement: "The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality".
He meant what he said. But that doesn't mean to say he was right. Take a look at Wikipedia. He gave his address on 21st September 1908. On 12th January 1909, less than four months later, he was dead. IMHO had he lived longer, he would have qualified the above.
Should it be interpreted as follows? Since both space and time are relative, observer dependent quantities, with the coordinates of both becoming mixed together under transformations between two inertial reference frames, this implies that [they] form a single 4-dimensional entity since neither space nor time exist independently from one another...
Most people will say yes it should. But I'm afraid most people are wrong. Because in this single 4-dimensional entity, in the block universe called spacetime, there is no motion. And we live in a world of space and motion*. Hold your hands up a foot apart and you can see the gap, the space between them. Now waggle your hands, and you can see motion with your own eyes. In this respect both space and time are empirical. But spacetime is not. It is an abstract mathematical arena. It is the "map". Not the territory.
(since, the spatial and temporal coordinates in one frame both become a mixture of spatial and temporal coordinates relative to another, and cannot be separated from one another).
There's nothing wrong with that. But think about it: you measure distance using the motion of light through space, and you measure time using the motion of light in your light clock. Then when you move, your measurements of distance and time change. One "rotates" into the other. And the underlying reason is trivially simple, see the simple inference of time dilation due to relative velocity. The Lorentz factor is just Pythagoras's theorem in disguise. And it works for you like it works for the parallel-mirror light clock because of the wave nature of matter.
Additionally, in special relativity it is the spacetime interval that is absolute
It isn't. A photon absolutely does not go from A to B instantly. That zero interval is not absolute. And when you go on a fast out-and-back trip and I stay at home, our spacetime intervals are the same merely because the light-path-lengths in our parallel-mirror light clocks are the same.
implying that it is a 4-dimensional spacetime that one should consider in order to preserve any concept of an observer independent reality, with observer independent measurable physical quantities (such as the spacetime interval).
No. One should consider space and motion to preserve the concept of observer independent reality. The mathematical model called spacetime can assist with this, but we live in a world of space and motion, not in a static block universe. The map is not the territory.
- See relativist Ben Crowell's answer here where he said "Objects don't move through spacetime. Objects move through space".