Add last move time to game PGNs and info where a date and time are returned

The scenario is as follows: a correspondence game is being played, a move every few days as an extreme case. When one gets the list of the user's games, they are ordered depending on the time they started. When the game ends, months from when is started, you don't even see it in any recent game lists.

I believe the information of last updated, not created, should be used for ordering. Even if it is not, it should be available for reordering client side. At this time there is no way to get the information of the last move other than request the clock information and add the time for each move to the start of the game. Moreover, correspondence games [don't even export the clock](https://github.com/lichess-org/api/issues/653) information!

Review the API documentation for game lists, PGN exports, and responses that return date and time information. Compare the available timestamps with the issue's correspondence-game scenario, then identify where a last-move time could be exposed and verify that completed games can be reordered from the returned data.

Written by the indexing model from the issue text.