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when things get heavy
I can't speak to the medical/anatomical side of things, but surely there is a very useful psychological benefit to experiencing yourself pushing your treshold up another notch. A boost of confidence that will hopefully carry through to the hypertrophy work you will do at the end of the session, so a net benefit overall even if you were indulging with 3 - 5 min rests during the T1 exercise at the beginning of the session.
For heavier strength work - rest as fully as is possible / needed for you. Generally 3+ minutes minimum. I'm usually 3-5, 5+ for when things get heavy, or I'm on the last few of a large amount of sets.
For hypertrophy + assistance work - generally shorter rest periods, as you say, more stress, more hypertrophy.