D.B.
Some of this - very little - is relatively easy to manage: your stepson keeps his toys in his room or behind a child gate (even those adjustable pens for puppies would work). He can get over the barrier, the baby can't. So put his stuff out of reach, or put her stuff inside the area, either one. But enforce boundaries, not separate rooms. If he leaves his things where she can get them, it's his fault. But the choking hazards would worry me.
The attention-seeking when there's a baby - normal. But she's 10 months old so this is getting old.
The food? You CAN make healthier options, like your own nuggets and oven fries which are delicious and nutrition-packed. I've done it for 2 stepkids, one bio kid, and 4 picky grandchildren. Message me if you want the recipes. Is that what he eats at his mother's house? No? But if the adaptations won't work? Then who is buying the sugar, the packaged nuggets, the chips, the candy? Who is cooking the unhealthy meals? You? Then stop. Your husband? Then that brings me to the hard part.
You don't have a stepson problem. You have a husband problem. Your husband wants to be the Party Dad, the Weekend Warrior. He doesn't want to be the parent. He wants to be the buddy. He's making this about HIS feelings instead of HIS parenting! He's not "sensitive" - he's in denial because he won't talk to you, his wife and supposed best friend. You're walking on eggshells because you don't want him to be sad.
So, you have a problem with the stepson, but you're also getting a preview of parenting of your daughter: you're going to be the bad guy, always, and he's going to be the pal, always. You say you see it already in your daughter. So, yes, she will be jumping on furniture and so on, refusing food, demanding a second meal of junk.
BTW Your husband's excuse that he "only has him 3 days a week"? That's almost half time! That's 40%, damn close to 50%. So that's bogus. What else is bogus? That this behavior is normal "for boys" - it's only normal if it's allowed. Boys get permission and excuses, girls get expectations. If you and your husband allow yelling and furniture jumping and indoor cartwheels, that's on you, not on your stepson. Unless your stepson has a diagnosis of ADHD or something like that, this is a parenting fault and not a kid fault.
Marriage counseling asap. Parenting classes asap. Otherwise you've got 18 years of hell in front of you, with both kids unable to respect rules.