Currently there are options for default, Raid, Mythic, PVP, Dungeon, Heroic.

I would like an option for Team. This option will only be used when the player is in a Team(group), but not in one of the others: Raid, Mythic, PVP, Dungeon, Heroic, etc.

The check for this is on zone change. IE when you zone it makes the check and it returns a value for Battlegrounds, Raid/Dungeon difficulty. How do I evaluate "Team"?

First, if this ends up being too difficult don't worry about it.
There are a lot of events that fire related to a party.
Another addon, Jamab, uses the following ones:
PARTY_INVITE_REQUEST
PARTY_LEADER_CHANGED
Another one is:
PARTY_MEMEBERS_CHANGED

Again, don't worry about it if is too complicated or too unreliable to detect.

Im doing some work in this area for 2.2 and talent based options so will add this in.