chore(telemetry): make logs less noisy and more clear

[mabdinur]

Partially Resolves: #10842

• Removes exception traceback from telemetry client logs. We should not generate a traceback everytime we fail to send telemetry payloads to the agent. This traceback is noisy and not actionable.
• Updates telemetry client log message to clearly state that instrumentation telemetry failed to send and not user telemetry (ex: traces, logs, metrics).

Checklist

• PR author has checked that all the criteria below are met
• The PR description includes an overview of the change
• The PR description articulates the motivation for the change
• The change includes tests OR the PR description describes a testing strategy
• The PR description notes risks associated with the change, if any
• Newly-added code is easy to change
• The change follows the library release note guidelines
• The change includes or references documentation updates if necessary
• Backport labels are set (if applicable)

Reviewer Checklist

• Reviewer has checked that all the criteria below are met
• Title is accurate
• All changes are related to the pull request's stated goal
• Avoids breaking API changes
• Testing strategy adequately addresses listed risks
• Newly-added code is easy to change
• Release note makes sense to a user of the library
• If necessary, author has acknowledged and discussed the performance implications of this PR as reported in the benchmarks PR comment
• Backport labels are set in a manner that is consistent with the release branch maintenance policy

[github-actions]

CODEOWNERS have been resolved as:

ddtrace/internal/telemetry/writer.py                                    @DataDog/apm-core-python
tests/telemetry/test_writer.py                                          @DataDog/apm-python

[pr-commenter]

Benchmarks

Benchmark execution time: 2025-01-06 19:44:28

Comparing candidate commit 9b9cd50 in PR branch munir/make-telemetry-less-noisy with baseline commit 81208cd in branch main.

Found 0 performance improvements and 0 performance regressions! Performance is the same for 394 metrics, 2 unstable metrics.

[datadog-dd-trace-py-rkomorn]

Datadog Report

Branch report: munir/make-telemetry-less-noisy
Commit report: 5dad21a
Test service: dd-trace-py

✅ 0 Failed, 87 Passed, 1468 Skipped, 4m 11.53s Total duration (35m 20.98s time saved)