Cleanup dead tracing code

[mcpherrinm]

Description

While investigating Vitess tracing code for migrationg to OpenTelemetry, I found that NewClientSpan was dead code, and that there were some references to the now-removed Start function.

Related Issue(s)

Fixes #19124

Blocks #19093
Related to #17341

Checklist

• "Backport to:" labels have been added if this change should be back-ported to release branches
• If this change is to be back-ported to previous releases, a justification is included in the PR description
• Tests were added or are not required
• Did the new or modified tests pass consistently locally and on CI?
• Documentation was added or is not required

Deployment Notes

This is a cleanup which should have no functional changes

AI Disclosure

All code was removed by hand.

[vitess-bot]

Review Checklist

Hello reviewers! 👋 Please follow this checklist when reviewing this Pull Request.

General

• Ensure that the Pull Request has a descriptive title.
• Ensure there is a link to an issue (except for internal cleanup and flaky test fixes), new features should have an RFC that documents use cases and test cases.

Tests

• Bug fixes should have at least one unit or end-to-end test, enhancement and new features should have a sufficient number of tests.

Documentation

• Apply the release notes (needs details) label if users need to know about this change.
• New features should be documented.
• There should be some code comments as to why things are implemented the way they are.
• There should be a comment at the top of each new or modified test to explain what the test does.

New flags

• Is this flag really necessary?
• Flag names must be clear and intuitive, use dashes (-), and have a clear help text.

If a workflow is added or modified:

• Each item in Jobs should be named in order to mark it as required.
• If the workflow needs to be marked as required, the maintainer team must be notified.

Backward compatibility

• Protobuf changes should be wire-compatible.
• Changes to _vt tables and RPCs need to be backward compatible.
• RPC changes should be compatible with vitess-operator
• If a flag is removed, then it should also be removed from vitess-operator and arewefastyet, if used there.
• vtctl command output order should be stable and awk-able.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 69.87%. Comparing base (fa770f9) to head (1c0afa1).
⚠️ Report is 6 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #19092   +/-   ##
=======================================
  Coverage   69.87%   69.87%           
=======================================
  Files        1613     1613           
  Lines      216002   216017   +15     
=======================================
+ Hits       150939   150950   +11     
- Misses      65063    65067    +4     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[mcpherrinm]

CI failures looked spurious, and this PR was a bit stale, so I rebased on main.

I've added a linked issue per NeedsIssue tag.