refactor(Analysis): golf Mathlib/Analysis/Complex/ValueDistribution/LogCounting/Asymptotic

[yuanyi-350]

• shortens one_isLittleO_logCounting_single by deriving it from a theta estimate for log r - log ‖e‖
• shortens logCounting_isBigO_one_iff_analyticOnNhd by reusing divisor_nonneg_iff_analyticOnNhd directly

Extracted from #37968

[github-actions]

PR summary 48f66c0814

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

No declarations were harmed in the making of this PR! 🐙

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

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No changes to strong technical debt.

No changes to weak technical debt.

[yuanyi-350]

I ran a profiler comparison for the changed declarations in this PR.

Results (seconds):

• one_isLittleO_logCounting_single: 0.203687 -> 0.032370 (-84.1%)
• logCounting_isBigO_one_iff_analyticOnNhd: 0.420270 -> 0.051027 (-87.9%)

Overall:

• both proofs got substantially faster