What will happen if my flight gets cancelled after my 90 days is up and I am already at the gate?

I've directly observed this before, in Germany.

Passengers who needed visas due to force majeure were issued 24-hour Schengen visas at the consular office inside the Frankfurt airport.

There is a duplicate answer with citations from the Schengen Code here.

In a sense you still are, you are on the territory of a Schengen country, its law fully applies, if you did anything that would justify it, you could be arrested by the police, etc. The airport, even the area after the exit passport check is not some sort of extraterritorial area out of reach of the country's laws.

That said, if you stay airside in the sterile departure area, I don't see how you could possibly be deemed to have breached the conditions of your visa. You already have an exit stamp with the proper date and would not have any problems the next time you applied for a visa or enter the Schengen area. If the airports has such facilities, you should press the airlines to offer you lounge access or an airside hotel room to wait for the next flight.

Now, if you need to go through the passport check again, say, to spend the night outside of the airport or catch a plane at another airport in the vicinity, things become more complicated. There is a provision to extend a Schengen visa (article 33 of the visa code) if you have a serious reason but my reading of the regulation is that this is in principle only possible if the new stay would not lead you to exceed the global 90-day limit for short stays in the Schengen area.

If someone needs to stay longer than that, member states still have the possibility to issue a “limited territoriality visa” (article 25) and they may in any case issue a visa at the border (article 35). Both of these are intended as exceptional procedures but the authorities have some leeway in judging what's an exceptional case. Combining articles 25 and 35 would therefore seem to be a fully legal way to grant you some more time in the country where you presently are, at the cost of a bit of paperwork and possibly a fee.

I can also imagine that some border guards would be confused about all this and I am not entirely sure that it would happen smoothly.

This has happened to me personally, you either get a 24 hour temp visa or they escort to a hotel at the airport and back again the next day, both happened to me, FWIW other countries mostly do the same it happened to me in china and in Australia as well, as long as you go with the airline staff to immigrations they will sort you out