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I see your point, kind of trippy to think about. Is time constant?
As Einstein said, time is relative. But that only means it is relative to different circumstances.
Moving at light speed time stands still, and the theory is that inside a black hole time also stands still.
So being at a stationary position in non gravity space is the fastest time will go.
But lets make it simple, and consider weather time is a constant on earth, at least within a margin we are not able to perceive.
And to that question the answer is that yes time is constants, because changes in the speed of time are universal and affect everything equally.
Meaning that the relative time we perceive is constant.
BUT on the other hand, time is different to a satellite that orbits the earth, because the faster movement slows down time, but the lower gravity accelerates it. Which makes it necessary for GPS satellites to compensate for that to make accurate positions possible.
Anecdotally the GPS system was originally financed and implemented by the US military. And the generals did not believe this, so they claimed the system to compensate was unnecessary, which of course it turned out the scientists were right, so they had implemented the system to compensate anyway, and could turn it on, when they had proved to the generals that it indeed was necessary.
https://www.gpsworld.com/inside-the-box-gps-and-relativity/
This just made me think of something... Have we ever proven through measurement the speed of light is constant? For example every test I can seem to find requires measuring it both ways. How do we know it's not faster in one direction? Wouldn't we still get the same measurement if we can only measure that way?
The limit of speed of light is a property of space-time, not a property of light.
Another way to understand it is that it is the maximum speed of causality. The limit doesn't go only for light, but for instance also for gravity, which AFAIK is also proven by the measurement of gravitational waves.
The reason only light can achieve this speed is that it is massless. Because if light had mass, it would have infinite energy, and take infinite energy to achieve the speed of light.
There are numerous explanations for how 2 objects moving at the speed of light still only approach each other at the speed of light.
Take a look at Youtube, there are many good videos explaining relativity in general and speed of light in particular.