chore: Undo recent changes to EngineService controller update handling

[Gudahtt]

Description

A recent PR (#17685) migrated to a new storage system for controller state. This change required additional state change subscriptions, but in the process of setting those up, the "update Redux" step ended up inside of the persistence handler.

This is not ideal because it's semantically confusing (updating Redux is not related to persistence, it's how we update the UI), and it means UI updates are now slightly delayed (getPersistentState is now called each update before the UI is updated).

This PR reverts the changes to how Redux is updated when controller state changes without impacting the persistence handling.

Changelog

CHANGELOG entry: null

Related issues

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Manual testing steps

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Screenshots/Recordings

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[github-actions]

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