Two cars, both moving forwards, can still move in different directions! So does "forwards" exist? Not as a global direction, but once you have picked an orientation it is a useful label for a distinguished axis.

Time is like that. Pick a velocity, and then time is a distinguished axis in the coordinate system you overlay on spacetime.

Measures of speed can make no sense even when you allow for time :)

https://en.wikipedia.org/wiki/Inertial_frame_of_reference

In the same way speed depends entirely on your frame of reference, so does our perception of time.

But it doesn't make sense. OP is saying that there is no absolute measure of time, it depends on the frame of reference of the observer. Therefore there is also no absolute measure of speed.

Correct. A fly on the seat of your car travels 0 m/s with respect to the car and to you, but travels, say, 30 m/s with respect to the road. Speed (and velocity, for that matter) always needs a reference to be meaningful.