It needs to be built up tutorial style, while actually being designed around the mechanics. Sometimes people just add mechanics during game development which leads to an inferior experience, especially when earlier parts of the game should have the updated mechanics.
Yeah, I agree about "building up" the game around its core mechanics. New mechanics that are added too late in development (or too late in a game's main questline) can feel "slapped on" or half-baked.
I think it may also boil down to how the content is "locked". There's a big difference between stuff that is locked by being "hidden" and stuff that is actually "locked". So, I feel like "hidden content is gradually revealed by exploration" should be a fourth category in the poll.
The original Dark Souls is a good example of "hidden" paths that aren't really locked. With the right choices, like five different paths can be accessed from the beginning of the game (skeleton key, my beloved). But the level design still funnels new players down particular routes. It's the best of both worlds.
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While Dark Souls isn't really a sandbox game, the same principle applies. IMO, the best sandbox games are the ones where parts of the map are initially hidden by fog of war or blocked doors, and then revealed through gradual exploration, either by simply pressing "explore" (like in Corruption of the Champions, where there is a fixed chance to discover a new area each time you explore), by finding the right path out of several options, or by using the right object (as in many old school adventure games and RPGs). If the map is visible, then the events on different tiles should still have to be figured out, like in Tales of Androgyny.
The secret paths and sewers in Degrees of Lewdity are another good example of clever route design, where even distant areas are accessible from the start, but become easier and less time-consuming to get to as you learn better routes through the world.
How much content is "hidden" and how much is actually "locked" by bosses or obstacles at the start of a game varies by genre. If the game is a Metroidvania or an old school adventure game, then finding new powers/objects or solving puzzles usually open up new ways of movement, leading to new areas. Like, finding a grappling hook that allows you to reach high places you could see at the start but couldn't get to, or gauntlets that let you move boulders, that sort of thing. When done right, there's something very satisfying about finally getting past obstacles that seemed impenetrable at first. It's the same principle that can make returning to old areas fun in an RPG--a sense of progression and discovery.
So, that's what I like--some combination of "hidden" paths revealed through exploration and "locked" obstacles overcome by progression.
Games where large chunks of content are gated by purely quests, achievements, or finishing certain storylines tend to spoil that sense of progression by making it feel too artificial. This is particularly true in games where the visual novel elements clash with the sandbox elements, like Corrupted Kingdoms, where certain characters are locked behind completing other characters' routes.
On the other hand, open world games with total free-roaming can feel a bit empty or unrealistic if there are too few impediments to travel in the overworld, or if the overworld is too big and samey. For example, in Elden Ring, the big, open frozen plateu near the end of the game is much less fun than the multiple routes and barriers leading up to the castle near the beginning of the game.
Also, in most sandbox games, forced fast travel kind of breaks my immersion. It can be nice to have some form of fast travel as an option, but if the world is interesting enough, it's better to be allowed to explore it naturally. When combined with a hub area (like in Dark Souls 2) or a mission-based system (like in Darkest Dungeon), fast travel works well for games where the actual combat and exploration within a particular zone is linear and slow-paced, and you see a lot of the environment. In games where movement on the overworld map is more open, fast travel kind of sucks. Like, in Skyrim and Red Dead Redemption, the fast travel system is more of a crutch for the wacky way that hostile encounters spawn. Like, jeez I'm sick of constantly getting attacked by wolves and bandits. Oh well now that this set is dead, time to teleport away before more show up. THAT's the kind of fast travel that sucks. There's a reason why Morrowind still has a cult following (in spite of the constant cliff racer spam)--if the environment is interesting enough, then slow travel is best.
TLDR:
1. Game mechanics should be built up gradually and thoughtfully.
2. Hidden content revealed through exploration is generally more fun than quest-locked content.
3. If content is actually locked behind bosses or other obstacles and not just hidden at the start, then there should be a sense of meaningful progression like in a Metroidvania.
4. Locking a character or region behind another character's route is usually annoying, especially in a sandbox game.
5. Fast travel is a mixed blessing at best. In a chill game with interesting environments, a slow tour is more satisfying than just teleporting around.
Those are my two cents, anyway!

Your mileage may vary.