While an argument could be made for meaningful difference existing between 2D and 3D Zelda design (the top-down perspective both limits the world design and augments spatial awareness that benefits a spatial-puzzle focus), "classic 3D Zelda" feels uniquely defined by its concessions and limitations.
BotW was the first HD Zelda game, and the first in the series to even be able to harness the associated benefits (bigger game sizes, ways games can be streamed/loaded, etc.). Before that, the older 3D games had to be designed around "what can we fit in this individual room?" and "how can we approximate a sense of grandeur in Hyrule Field when it's actually quite tiny?"
In OoT, the path to Death Mountain and Goron Village is just that: a path. Entirely linear with background visuals to make it seem like the player is travelling far through treacherous terrain, all split up by transitional loading screens. Of course the puzzles and traversal and boss battles had to all be condensed in dungeons because you can't have a seamless open landscape with all those regions on the N64.
However ... in BotW, getting to Death Mountain became a memorable experience for me all on its own since I immediately tried getting to the volcano, only to learn the heat was too great, and had to quickly retreat before stumbling across the Goron hot springs and an old Goron who essentially directed me back to their town where I could purchase protective armour. That level of meaningful traversal was consistent throughout the whole game, and even when I could see its limits and shortcomings, those feelings were second to the uninterrupted sense of adventure throughout large swathes of my time with BotW. The meaningful interaction between the player and the dungeons from games past is now all over the open map.
All of the things I see mentioned as hallmarks of "classic 3D Zelda" are things that can be layered atop BotW's approach. Dungeons filled with puzzles that create a contained arc of progression and exploration can work in BotW (and already existed there with the divine beasts, just with room for improvement). Expanded creature/enemy variety would sit well alongside the tangibly varied biomes (tangible in the sense that certain places are hot and arid, which affects the player/aspects of the game world, and which could lend itself to housing camel-like creatures/enemies that could store water in their humps). More gadgets would be further opportunity to interact with the fleshed-out physics and "chemistry" systems already present.
BotW achieves perhaps the greatest sense of fundamental freedom and adventure in the series, and I see no reason to create a dichotomy between it and the particular strengths of the "classic 3D" entries because BotW didn't eschew those strengths. If anything, it merely made room for them within its expanded scope.
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