How would you deal with it if you wanted to discuss polyamory with your partner but he is going through a busy/tough time in his life and doesn’t seem to have the time or energy to talk through big changes like that right now?

It sounds like you know what your partner needs - time. Is this busy/tough time looking like it will come to an end anytime soon? If so, it’s best to wait it out. Unless this feels like an emergency for you, like you feel like you can’t stay in this relationship much longer without opening it up, try to be patient.

Do your best to support your partner through this tough time - maybe do a little extra to help out with chores, check in with him about how you can be there for him in all this - and trust that your relationship will ride this out until he’s in a calmer place.