Assign new players to the first team with no players

But only if the game has already started, (since with an unstarted
game, all players are intentionally unassigned so that any player can
go first).

If there is no team that has no players, the new player will be
unassigned, (and will instead be a spectator until they join a team).

This logic is designed so that a game in which the precise number of
people were invited to play, (most notabl, a two-player game), these
players will be automatically assigned to teams as soon as one player
makes a move, (regardless of whether the players joined the game
before or after that move).