From what I understood from this (Multicolumn indexes pg 9.6 (but same up to 12) the indexes can be used when the query involves columns from the index, going from the left to right.

In this case the second index on organization_id doesn’t give you anything extra since the leftmost column of the unique index you created before, is that same column.

Here you wouldn’t need a team_id index, but you would need a user_id if you are planning on querying the teams_users table solely by user_id (without team_id that is).
The team_id being the leftmost column declared on the unique_index would be used when a query containing a team_id column is made.

Theoretically this applies to indexes with more than 2 columns too.
E.g.

unique index on a, b, c
Means that pg can use the index on a query containing:
a
a,b
and a,b,c

(though it still goes through the planner ofc, so it might not use it, but that wouldn’t be because it can’t, at least this is my reading from the docs, it also means that the order in which you declare the columns for the index plays a role too)