For your first transformation with the spell, Shapechange says:
You assume the form of a different creature for the duration...Your game statistics are replaced by the statistics of the chosen creature, though you retain your alignment and Intelligence, Wisdom, and Charisma scores.
The statistics of the creature include abilities that are restored with time, whether they are per day, per rest, or have a rolled recharge each turn. Since that creature, which has appeared de novo and never existed before, has not used any of its abilities, all of them are at 'full' and freely available.
Now suppose you want to use these abilities, and then use Shapechange to re-assume the form of a similar creature so as to restore the abilities for repeated use. Is this possible?
Our favorite Hobgoblin's answer correctly points out that this depends on what the spell means when it uses the word 'different':
During this spell's duration, you can use your action to assume a different form following the same restrictions and rules for the original form,
If the second-and-beyond transformation is to a different form, what is it different from? The caster's true form? All forms previously assumed? The most recent form? Any of these meanings are possible within the normal English meaning of different, but they will give alternate answers to whether one casting of the spell can be used to repeat forms, or to go from one form to a new version of the same form.
However, I don't think that shapechange uses "different form" in the ambiguous sense of normal English usage. Rather, it uses it in a way that is idiosyncratic to the spell, but internally consistent throughout1.
Indeed, shapechange uses "normal form" to refer to the caster's true form, "new form" to refer to any form assumed by transformation (including the first one), "original form" to refer to what is obtained in the first transformation, only, and it uses "different form" to refer to any transformation after the first. In this sense 'different' means 'a form that is different from the one used in the first transformation', and it is necessitated by the hp rule. It says:
...you can use your action to assume a different form following the same restrictions and rules for the original form, with one exception: if your new form has more hit points than your current one, your hit points remain at their current value.
What this means is that in the very first transformation, you do assume the hp of the new form, while in all subsequent transformations you do not, if doing so would increase your hp. Thus what is 'different' is that in subsequent forms your hp cannot increase.
Given that this is explicitly stated to be the only limitation of subsequent transformations, you can indeed transform into a 'fresh' version of a form with regards to abilities, and can use this to restore functions, whether you are cycling through a series of repeated forms or just re-assuming the same one over and over again.
1 At least, I have to assume its use of these terms is internally consistent. If they are synonyms with ambiguous but inconsistent meanings, there is no way to know the intent of the spell.