[tests] improve logging and documentation in interface_rest.py

Summary:
Partial backport of core PR12766 (commit 3fd4490)
https://github.com/bitcoin/bitcoin/pull/12766/commits/3fd4490db1381c0a68112edfb2b2e5f5906dab8c

Depends on D3765

Test Plan:

./test/functional/test_runner.py interface_rest

Reviewers: #bitcoin_abc, deadalnix

Reviewed By: #bitcoin_abc, deadalnix

Differential Revision: https://reviews.bitcoinabc.org/D3766