More specifically, my goblin has a medium wolf Bonded Mount right now, at level 7 that will grow to large size. Do I need a new mount then, or will it still work?
I can always slap an item with a permanent Reduce Animal on it, I guess, but that would be silly.
You can choose to not increase it's size.
Instead of taking the listed benefit at 4th or 7th level, you can instead choose to increase the companion's Dexterity and Constitution by 2.
Humans can ride elephants. Humans are medium, elephants are huge. You must be at least one size category smaller than your mount. Nothing, to my knowledge says that you must only be one size category smaller than your mount.