Block Hooks: Inject hooked blocks into modified templates and parts

[ockham]

Using the new technique of storing information about whether or not a hooked block should be considered for injection or not, extend said injection to encompass modified templates and parts.

Follow-up to #5712.

Trac ticket: https://core.trac.wordpress.org/ticket/59646

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[github-actions]

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[github-actions]

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[ockham]

This is one of the major changes planned for 6.5 and has been in the works for a while. It has been discussed quite extensively on the accompanying ticket, and most work has happened on preparatory changesets such as https://core.trac.wordpress.org/changeset/57157 and WordPress/gutenberg#58553. Unit test coverage in this PR should ensure that it works properly.

I'll commit shortly 🙂

[ockham]

Committed to Core in https://core.trac.wordpress.org/changeset/57594.