[results-processor] Improve logging/security of secrets access from the results-processor

[gsnedders]

Accessing secrets to the results-processor is being added in #4025; see https://github.com/web-platform-tests/wpt.fyi/pull/4025/files#r1786456351 for discussion here.

Ideally we'd have both:

• better guarding of accessing this (but ideally without entirely tying the processor module to the Flask front-end, as @main._internal_only would imply — which also would add a circular import), and
• more detailed logging as to what exactly is accessing the secrets (run_id, uploader would be obvious — or maybe we should do this for all logging from the processor via a LoggerAdapter?)