I think since the card says that only you skip your draw step that only you do. That sort of effect doesn't effect your partner because otherwise the entire starting team would skip their draw step instead of just the primary player.
If an effect gives a player an extra turn or adds a phase or a step to that player’s turn, that player’s team takes the extra turn, phase, or step. If an effect causes a player to skip a step, phase, or turn, that player’s team does so. If an effect causes a player to control another player’s turn, the controller of that effect controls the affected player’s team’s turn.
It isn't intuitive to me, but it's clearly the way the rules work.
I think it's intuitive when you think that all the phases and steps in the turn are shared by the team in 2HG. If you're playing something that takes one of those phases or steps away, then there's nothing to share, so no one on the team gets it.
If an effect gives a player an extra turn or adds a phase or a step to that player’s turn, that player’s team takes the extra turn, phase, or step. If an effect causes a player to skip a step, phase, or turn, that player’s team does so. If an effect causes a player to control another player’s turn, the controller of that effect controls the affected player’s team’s turn.
It isn't intuitive to me, but it's clearly the way the rules work.
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