(Posting as answer, because it's long, has formatting and at least offers a partial solution.)
I would say we should allow as much specification as possible without getting name collisions. This is a complicated topic and there are a lot of things the same between all versions, but also a lot of things different between them, so I would say: The more tags, the better. Otherwise people would have to specify this in every question anyway.
- minecraft for everything: Java, together, PlayStation, raspberry, education, …
- minecraft-pocket-edition for questions specifically about Android, iPhone, iPad, Windows Phone, etc. ports of Minecraft (can be important, because e.g. some graphics settings differ)
- minecraft-windows-10 for questions specifically about Minecraft on the desktop port of Bedrock Edition (or maybe including Windows Phone?)
- minecraft-legacy-console for the legacy port on PlayStation
- minecraft-console for the consoles that can play with the others (the ones developed by 4J Studios)
- minecraft-bedrock for the windows 10 and mobile versions, the ones that actually share most of their code
- minecraft-education for the education edition
- minecraft-raspberry-pi for the discontinued Raspberry Pi edition
- minecraft-java for Minecraft Java edition
- minecraft-multiplatform, minecraft-together, minecraft-unified and minecraft-cross-compatible for the Pocket, Windows 10 and console and whatever else is included in the "Better together update". Four variants, because this should be the main tag for questions about this game and people should be able to find it.
- And then also one tag per device, like Wii U, PS4, iPad, even Linux and Mac for the Java edition, because there can for example be launcher issues specific to one operating system. This could act like the "environment" field on the bugtracker.
One more question: What to do with the questions that already have these tags? For example some of those that have the tag minecraft-console-edition now are e.g. on the Wii U, which will be the "together" edition, but some are about PlayStation that won't get that update.