200GS is a bit oldschool. But I found this:
200GS specs are on 59/68. Looks like the rear derailleur came in too varieties, long cage and super-long cage, the former having max sprocket size of 30T and a total capacity of 36T and the latter having a max sprocket size of 32T and a total capacity of 38T. Total capacity is difference in tooth count between smallest cog + small chainring and largest cog + large chainring. So, it looks like you’re exceeding the specified maximum but Shimano is historically conservative with those specs and if it works, it works. You’re probably also exceeding the total capacity spec because you’re probably at 40 with what’s most likely 28/38/48 rings up front, but the consequences of that are just that if you’re in small/small the derailleur doesn’t have enough wrap to keep the chain tight. Since that’s another gear you never use in practice, doesn’t matter much.
The chain tracking slightly beside isn’t a big deal. It just means that the cassette on the new wheel isn’t sitting in quite the same place as the old one relative to the frame dropouts. You can tweak the positioning of the derailleur by turning the barrel adjuster where the cable enters the rear derailleur, or if that doesn’t have enough travel, letting out/taking in a bit of cable where it clamps on the derailleur.
The derailleur should be pretty much fully stretched out in big/big. It’s not like you should ever be in that gear combination anyways.
And finally, if that spec sheet is to be believed, 200GS was freehub/cassette in 7sp configuration and freewheel in 6sp.