proxy: Improve logging

[khanova]

Problem

It's unclear from logs what's going on with the regional redis.

Summary of changes

Make logs better.

Checklist before requesting a review

• I have performed a self-review of my code.
• If it is a core feature, I have added thorough tests.
• Do we need to implement analytics? if so did you add the relevant metrics to the dashboard?
• If this PR requires public announcement, mark it with /release-notes label and add several sentences in this section.

Checklist before merging

• Do not forget to reformat commit message to not include the above checklist

[github-actions]

2760 tests run: 2642 passed, 0 failed, 118 skipped (full report)

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Code coverage* (full report)

• functions: 27.9% (6396 of 22958 functions)
• lines: 46.3% (44731 of 96516 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
f962772 at 2024-04-17T11:40:50.843Z :recycle:}