Move headers-direct-fetch logic into own function

Summary:
And move headers direct fetch to end of ProcessHeadersMessage

Review tip:
git show --color-moved=dimmed-zebra --color-moved-ws=ignore-all-space

This should show only linter changes due to reduced indentation in the moved code block.

This is a partial backport of core#25454
https://github.com/bitcoin/bitcoin/pull/25454/commits/29c45185223441943ab610e62937a118c7c3a5b2
https://github.com/bitcoin/bitcoin/pull/25454/commits/2b341db731793844f12944363186edea23eabdeb
Depends on D14908

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D14909