Enter Ireland as non-visa national and proceed to UK - what is the allowed duration of stay?

I am a non-visa national planning to visit Ireland and the UK with entry through Ireland and onward to UK without passing through immigration control.

Does the duration of stay I am given in Ireland cover my total stay in the Common Travel Area? Basically if I am unfortunate and say given only 1 week upon entry into Ireland (instead of the standard 90 days), do I have to depart the UK before the 1 week is up, or do I automatically get the standard 90 day leave to enter once I cross over into UK?

This much I know:

When someone transits via Dublin into the UK they do so on a 90 day leave-to-enter issued by the Republic of Ireland. This allows the holder to move about the Common Travel Area.

The leave-to-enter does not automatically become a six-month UK leave-to-enter by crossing a border. Regardless of where they are the person becomes an overstayer on the 91st day.