How can you have awareness of time if you have no memory of 1 second ago?
Perception of time is part of memory that "now" is different than it was 1 second ago.
Time, as experienced by a human is a product of sensory processing and memory. Short term and working memory. There is bit of research on manipulating the perception of time by different tasks and events.
https://www.popsci.com/how-time-seems-to-stop/
It's the experience of change.
This is why the speed of time can be altered based on tasks and attention.
https://en.wikipedia.org/wiki/Chronostasis
Time , as defined by physics , is its own thing independent of an animal's perception of time.
Like how vision is from light. But light is not vision.
We do have a circadian rhythm. So do all animals.
This is an internal clock that regulates the body.
https://en.wikipedia.org/wiki/Time_perception
https://en.wikipedia.org/wiki/Circadian_rhythm
Likewise , basic small time tracking appears to be largely done by the brain stem, limbic system, but probably the cerebellum. But not the cortex (higher function brain regions)
It is generally believed "consciousness" is a process of the cortex as this is where complex cognitive tasks are done.
"Experiments have shown that rats can successfully estimate a time interval of approximately 40 seconds, despite having their cortex entirely removed.[25] This suggests that time estimation may be a low-level process.[26]"
There is also a human disorder where the loss of time estimate ability can occur. Not completely independent of memory disorders. Short term memory is impaired.