Well I am ( or rather was ) a Metallurgist and Sparky has it correct.
Annealing in copper is simply a stress relief and if you think of it like that it should avoid confusion.
Annealing copper or tempering steels, both soften and both cooling rates are not important.
Hmm. I'm not quite buying that. Do they really make copper sheet that is too impure for a gasket and cannot be annealed? Isn't "full soft" just annealed copper? Aren't we going to anneal it anyway?
Copper sheet is made in a lot of different alloys for different purposes.
For roofing as an example there are grades that stay bright pink, grades that go dark brown & grades that go green.
Known in the trade as weatherproof ( stays pink ) or weathering ( goes green or brown )
None of these are suitable for making gaskets.
However any grade that is sold as "full soft" will be suitable which is why I made that comment.
Sheet copper with arsenic in it will heat treat and harden if you try to anneal it.
Same for chrome, vanadium and nickel and all of these are "micro alloyed" so typically contain less that 1% of the alloying element which technically is "pure copper" .
Even worse is that now a lot of copper is processed in China the compositions could be any where and you could be buying any sort of rubbish as most companies that shift manufacturing to China do not do it in order to produce a better higher quality product.
I would have to check but from memory any thing above 95% copper is allowed to be called "Pure Copper" depending upon the end use.
For thin section like rainwater fittings you want it to be hard.