Improve Server endpoint for fetching the game state

[merowin]

The implementation of the server function for fetching the game state (getGameState) is not ideal. The basic problem is that there can be multiple moves within a round, and it is not 100% clear at which point we should return the state (e.g. at the start of the round or at the end of the round, etc.).

For example for parallel moves variants, we want to display the staged moves of the current round, but not for past rounds. So we implemented it s.t. the start of round is returned for past rounds, and the latest state is returned for the current round. But I'm not sure if this system is sensible for all kinds of variants.
Also for variants without staged moves and such, the implementation is not as efficient as possible (we compute the game twice in the case that we fetch a past round).

Here are the points that we should think about / improve if possible:
1.) Is the current system sensible for all possible variants? (If not, what would be a better way?)
2.) Can we make the implementation more efficient? (E.g. avoid computing the game twice)

See also this conversation:

I used a naive solution for the gameState endpoint on the server, that is probably not as efficient as possible

🥳 looks good! For efficiency, I'm not too concerned, but feel free to open an issue (we could mark as "good first issue" since it seems relatively self contained, and isn't causing much harm as-is)

Originally posted by @benjaminpjones in #267 (comment)