Un-revert BUI PRs

[ElectroJr]

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This is a combination of two earlier reverted BUI PRs (#3102 and #3104).

The PRs had two issues. Firstly, player status/connection changes caused enumeration-modification errors (see #3110). This PR now just has a ToArray().

Secondly, content assumes BUIs have been initialized by the time the components start getting initialized. Previously this was just done in ISerializationHooks. Now, this PR just no longer removes those. Properly fixing this requires a larger content PR.

Requires space-wizards/space-station-14/pull/10608