As long as you haven't exceeded the 90-days-in-any-180-day-period limit, you haven't overstayed. What's illegal is staying longer than you should, not missing some stamps per se. Framing the problem in that way, the question becomes: Who needs to prove that you did or did not fulfill the conditions of your stay and how?
Article 11 of the Schengen Borders Code states:
If the travel document of a third-country national does not bear an
entry stamp, the competent national authorities may presume that the
holder does not fulfil, or no longer fulfils, the conditions of duration of
stay applicable within the Member State concerned.
So the burden is on you and border guards or the police may probably impose a fine or perhaps even deport you or add an entry to the SIS if your passport is checked somewhere in the Schengen area more than 90 days after your first entry and you didn't get any new exit/entry stamps in the meantime.
But the next paragraph is:
The presumption referred to in paragraph 1 may be rebutted where the third-country national provides, by any means, credible evidence, such as transport tickets or proof of his or her presence outside the territory of the Member States, that he or she has respected the conditions relating to the duration of a short stay.
You should therefore keep everything that shows you were outside of the Schengen area (the plane ticket of course but also rental agreement, hotel bills, work contract, official registration if there is one, etc.).
One thing I don't quite understand in your question is on what basis you are currently staying in Norway. Norway is part of the Schengen area so it's not true that “you technically haven't ‘left’” with scare quotes and adverb; you really haven't left at all, period. If your working holiday starts later than the 1st of September then you are actually overstaying because you have no legal right to be in Norway at this time under Schengen rules.
As far as I know, you are responsible for submitting visa applications in a timely manner and until the application has been processed, you must fulfill the conditions for short stay in the Schengen area. The fact that you entered Norway hoping to get a long-stay visa or that you applied for it before the end of the 90 days period does not necessary allow you to stay in the country until a decision has been made.
On the other hand, if you are staying under the one-year working holiday visa, then I assume the visa or residence permit will state the date on which its validity starts. Once you get it, it doesn't really matter if you had the document in your hands at that date, you can use it to demonstrate you had a right to be in Norway and show your ticket to prove you actually used that right.