Except, due to oddities of the random generation, galaxy 4 - that has 64 each democracies, communists, multigovs and anarchies ... and no corporates, confederacies, dictatorships and feudals.
(Having played around sticking non-canon galaxy seeds into the generator from time to time, in some ways the impressive bit is that Bell and Braben managed to find a cyclic set of eight which mostly did have a reasonable distribution of governments, mostly universal connectivity, and no other major weirdness)
Assuming you take anything in the first game's manual as definitive [1], the first game definitely takes place before the collapse of Galcop, and likely even before the possibility that it was weakening to the point of collapse was acknowledged.
The exact date wasn't stated at the time - it must be in or after 3110 AD, because that's the Inservice date on the Mamba; since it contains hostile Thargoids it must in the Elite Dangerous timeline be in or before 3151 AD.
[1] Comparing the published manual with Ian Bell's draft notes, the Galactic Cooperative (as opposed to Bell's more generic "Galactic Government") appears to be a Holdstock addition.