Ocarina of Time is already nearly perfect as is, so I think another remake is wholly unnecessary. The only thing I would change is to make the game significantly less forgiving. Like hero mode, heart drops should be done away with, only this should extend to bombs, arrows, seeds, sticks, and nuts too. This should also be considered “normal” difficulty, with the usual way now considered an easy mode. This makes each individual consumable significantly more valuable, which in turn gives rupees an actual use. This also makes the skulltulla sidequest far more worthwhile. Technically this is a change I would make to all of the classic games (in fact it’s one of the few things I think BotW legitimately does better than the games that came before it) but OoT was the first one to really struggle with this.
Just about every other issue I have with OoT is so minor that it isn’t even worth mentioning, so everything after this is less of a “what do I want in a remake” and more of a “what I personally would have done differently if I were designing this game in 1998.”
The biggest one is that I would change the locations of the Goron and Zora tunics. Both items are technically optional, but the average player would never know that since both of them are given to them for practically no effort. I would make new mini dungeons for them on the other side of the map, and make the game tell the player that they are technically optional. This gives the player a practical reason to challenge themselves that isn’t just “because I can.”
Similarly, I would loosen the restrictions on dungeon order a bit (as in just make it technically possible to do them out of order, but make it something you really need to know how to do), and add rewards for doing specific dungeons out of order. For instance, maybe place a block in the forest temple that can only be pushed by silver guantlets and guards a shortcut to the dungeon item, or add a “magic key” item that will unlock all doors but is only accessible via a secret location that is blocked off by a combination of specific items.
Finally, give the player more things to do as a child after they get the Master Sword. Preferably things that utilize the child-only items in more unique and interesting ways.