Does the tea card in sushi go apply to other tea cards if it's the largest set, including itself?
TL;DR = Tea cards are a set.  You scored 9 points.

From the Rules here


  End of the round: Count the number of cards in your largest (or tied
  largest) set of cards with the same background color. Tea is worth
  1 point per card in that set.
  
  Example: Chris has 1 wasabi, 1 squid nigiri and 2 salmon nigiri. These
  4 yellow cards are his largest set. His tea is therefore worth 4 points.


There is nothing in those rules that excludes tea from being the largest set.  If tea was prohibited from counting then it should be stated here.  It doesn't say that tea is not counted.

The key to your debate however is defined in the set up rules and the definition of 'set'


  Take all the other chosen sets of
  cards and shuffle them together to
  form a face-down deck which is also
  placed near the board.


All the group of cards in the game are defined as being in 'sets'.  This therefore this must include Tea.  As Tea cards are collected in a 'set' then it's entirely possible that your largest set is Tea. So if you have 3 Tea and your largest set is Tea then you scored 9 points.