Change tracingService methods to use contexts

[mcpherrinm]

Description

The tracingService interface has methods New and NewFromString that are called by trace.NewSpan and trace.NewFromString.

trace.NewSpan and trace.NewFromString take and return a context.
That matches what OpenTelemetry's API wants, but doesn't match the tracingService interface they call.

By making the tracingService methods use contexts, it'll be much easier to add OpenTelemetry for #17341 as the APIs are aligned.

Related Issue(s)

fixes #19125

blocked on #19092
blocks #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 should have no functional changes, though I don't know if anyone is depending on these public interfaces outside of the Vitess codebase.

AI Disclosure

No AI written code, though some AI use while implementing this interface for OpenTelemetry is what motivated the change.

[vitess-bot]

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[mcpherrinm]

I've looked at the CI failures and they don't seem related. Flakes?

(Except pull request labels, which I don't have permission to set)

[codecov]

Codecov Report

❌ Patch coverage is 70.58824% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 69.88%. Comparing base (fa770f9) to head (9de286e).
⚠️ Report is 15 commits behind head on main.

Files with missing lines	Patch %	Lines
go/trace/opentracing.go	44.44%	5 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #19093   +/-   ##
=======================================
  Coverage   69.87%   69.88%           
=======================================
  Files        1613     1613           
  Lines      216002   216020   +18     
=======================================
+ Hits       150939   150968   +29     
+ Misses      65063    65052   -11     

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