ResidentLeever: Randomizers are unofficial and it's not the same when it's not part of the design and leads to backtracking in an artificial way like that. In a MV you tend to have a repeated loopback structure where you backtrack with a new movement ability or a newfound shortcut as part of the progression, changing the gameplay and/or layout during the backtracking.
Bloodstained's randomizer *is* official, however. In the vanilla game, no mods applied, you can go into the menu that's called something like "extra modes", and one of the options, along with the Speedrun and Classic modes, is the Randomizer.
Also, I've seen the shortcut mechanic in games of other genres. Etrian Odyssey and Stranger of Sword City do this, for example.
ResidentLeever: Perspective can make a big difference but it doesn't necessarily change the main genre like structural differences I think. Link's Awakening and some others also have platforming so they get even closer to mv/platform adventure games
I'd argue that, for action games, overhead and side scrolling are different genres, and the platforming sections of Link's Awakening represent a genre change. In a way, it's not that different from the genre changes in The Guardian Legend and The Magic of Scheherezade (though the importance of the other genre varies, and tMoS's genre change is perhaps more drastic, particularly since your moveset changes drastically between the genres in that game).
(Note that I would argue that Mario 64 and Zelda: Ocarina of Time are not in the same genre as their predecessors; with that said, I note that the change was more drastic for Mario than it was for Zelda.)
On the other hand, for turn-based menu-based RPGs, perspective doesn't really matter, because you're not concerned with movement during battle. (If you are concerned with movement, it's an SRPG, which is its own thing, but even then Fire Emblem (overhead) and Final Fantasy Tactics (isometric with rotatable camera) are in the same genre.)