Bugzilla 1958070: More BrowserGlue simplification/splitting

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Bugzilla: https://bugzilla.mozilla.org/show_bug.cgi?id=1958070

Large set of changes. I only noticed this due to one issue, but I imagine it will cause more, so we should add to the following list:

_migrateUI content was moved to a new file. I think our own migrate logic depends on _migrateUI being called first, so we should make sure it hasn't been broken. We should consider moving our logic to the same file.

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