I feel like you are overthinking it a bit, entangled in semantics. You can take any process that has a fixed frequency (like a clock), and measure the change in frequency in different situations, from the same point of reference. Moving that device at different speeds or into different places in a gravitational field. This is why satellite clocks move at a different rate than those on Earth.

Practically speaking, that's really what we care about when we talk about the speed of time. If some process takes a certain amount of time to complete, sending it to space and back, without changing anything else about it, might make it complete earlier from our point of reference.

It is actually about seconds per second, and there is an inner and an outer second as you say. There’s nothing wrong with that, because it is always a relative difference between two frames of reference. There are the seconds for our point of view, and there are the seconds for the device we are sending to space and back.

I think you are struggling to understand how to measure the absolute speed of time, but there’s no such thing, it’s always a comparison, it is relative.