iwyu: Fix warnings in some modules in `src/` and treat them as errors #36844

Split from #36808.

This PR fixes includes in some files in the src/ directory, as needed for #36808. Its scope is intentionally limited to minimize potential merge conflicts.

The changes outside src/ add headers that were previously included transitively.

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External sites

• Code coverage & benchmarks: https://corecheck.dev/bitcoin/bitcoin/pulls/36844
• Ralph review <img src=https://review.fish.foo/assets/bitcoin/bitcoin/36844.png alt="Ralph review status"> https://git.fish.foo/bitcoin/bitcoin/pulls/36844#author-ralph

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Reviews

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Conflicts

Reviewers, this pull request conflicts with the following ones:

• #36843 _{<img src="https://drahtbot.space/ack_count/bitcoin/bitcoin/36843.svg">} (scripted-diff: [test] Add util/check.h includes for assertions by maflcko)
• #35642 _{<img src="https://drahtbot.space/ack_count/bitcoin/bitcoin/35642.svg">} (headersync: do parameter search at runtime by sipa)
• #35229 _{<img src="https://drahtbot.space/ack_count/bitcoin/bitcoin/35229.svg">} (refactor: Use CBlockIndex parameters as reference by optout21)
• #31260 _{<img src="https://drahtbot.space/ack_count/bitcoin/bitcoin/31260.svg">} (scripted-diff: Type-safe settings retrieval by ryanofsky)

If you consider this pull request important, please also help to review the conflicting pull requests. Ideally, start with the one that should be merged first.

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