qa: Read reject reasons from debug log, not p2p messages

Summary:
Partial backport of Core PR14119
https://github.com/bitcoin/bitcoin/pull/14119/files

Rationale for partially completing this out-of-order backport:

• We get the benefits of this change today with minimal negative impact on future backporting efforts.
• The original PR is a bit large and could do with splitting up the review. Only two additional lines of code are necessary to make this backport digestible in chunks (and then all TODOs can be removed once completed).
• Improves robustness for D3863

Depends on D3860, D3861

Test Plan:

test_runner.py --extended

Reviewers: #bitcoin_abc, deadalnix, Fabien

Reviewed By: #bitcoin_abc, Fabien

Subscribers: Fabien

Differential Revision: https://reviews.bitcoinabc.org/D3862