chore(proxy): demote more logs during successful connection attempts

[conradludgate]

Follow up to #9803

See https://github.com/neondatabase/cloud/issues/14378

In collaboration with @cloneable and @awarus, we sifted through logs and simply demoted some logs to debug. This is not at all finished and there are more logs to review, but we ran out of time in the session we organised. In any slightly more nuanced cases, we didn't touch the log, instead leaving a TODO comment.

I've also slightly refactored the sql-over-http body read/length reject code. I can split that into a separate PR. It just felt natural after I switched to read_body_with_limit as we discussed during the meet.

[github-actions[bot]]

5535 tests run: 5309 passed, 0 failed, 226 skipped (full report)

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Flaky tests (2)

#### Postgres 15 - `test_pull_timeline[True]`: [release-arm64](https://neon-github-public-dev.s3.amazonaws.com/reports/pr-9828/11937675276/index.html#suites/82004ab4e3720b47bf78f312dabe7c55/209132ee3785cb7/retries) #### Postgres 14 - `test_pull_timeline[True]`: [release-arm64](https://neon-github-public-dev.s3.amazonaws.com/reports/pr-9828/11937675276/index.html#suites/82004ab4e3720b47bf78f312dabe7c55/7ecc4a6d4eb28c6d/retries)

Code coverage* (full report)

• functions: 31.4% (7938 of 25310 functions)
• lines: 49.3% (62998 of 127803 lines)

* collected from Rust tests only

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_{The comment gets automatically updated with the latest test results
8ff8efadb0253cf618c612650348666c0c564111 at 2024-11-20T17:57:07.215Z :recycle:}