Carry On

Allows you to carry mobs. Must have nothing in your off hand and main hand to carry something.

Mobs will slow you down depending on how big the mob is, and you can't interact with anything while carrying a mob. Examples: operating doors, Inventory, workbenches, hot bar scrolling. You can ride a horse / minecart and swim while carrying a mob.

Travelling through dimensions while carrying something will not stop you from carrying it. (examples: nether/end, planetary travel.) I will mention that if you take a mob to an area where you need a set of armor to survive there that mob will be safe as long as you are carrying it, and/or they are wearing a piece of armor that can survive the area you are in. (example: the moon needing a space suit)