Fix various circular requirements, method redefinitions, etc.

This can become handy when we separate core code and formulae. For
example, we could use `cd $(brew --repo homebrew/core)` to go to core
tap path.

Closes Homebrew/homebrew#50346.

Signed-off-by: Xu Cheng <xucheng@me.com>

The code was sucking. To the extent that maintenance was hard. It's a lot
easier to work with code that is sensibly split at sensible boundaries. So
now it is more like that.

But the refactor is minimal. Because we don't want you to have more merge
hell than absolutely necessary.

If you merge you will need to pay attention to brew.h.rb (as it is deleted)
and bin/brew (as command logic is gone). It will be painful, but you will just
have to help git out by moving any changes around manually.

Note compatibility.rb. It ensures that any function renames or removals don't
break anything. We're pretty serious about backwards compatibility. And that's
because we encourage you to hack around with the innards. And we couldn't do
that if we would then just make stuff disappear behind your back.