Why is there a foursome in golf? When/why was it determined that a
group of 4 was appropriate for golf??

Match formats in golf are defined in the rules and only allow for the
following permutations:
Matches 
Single: A match in which one plays against another. 
Threesome: A match in which one plays against two, and each side plays one ball. 
Foursome: A match in which two play against two, and each side plays one ball. 
Three-Ball: A match-play competition in which three play against one
another, each playing his own ball. Each player is playing two
distinct matches.
Best-Ball: A match in which one plays against the better ball of two
or the best ball of three players.
Four-Ball: A match in which two play their better ball against the
better ball of two other players.

As  you can see from the definitions, a foursome is actually a type of
match rather than a number of people in a group.

Foresome in the United States has become a generic definition of a
group of four people playing a round of golf together regardless of
the type of match being played.

Since golf originally was played as a match play competition (A match
consists of one side playing against another over a stipulated round
unless otherwise decreed by the Committee. In match play the game is
played by holes) the tradition of the game has been to play a maximum
of 4 people in each group.

There are many economic and efficiency explanations for limiting a
group to a maximum of 4 players but that would be another question.