otelhttp: Deprecate DefaultClient

[KonstantinosTsitoumis]

makes defaultClient private and creates a function that initialises it only once.

created for issue: #8131

[linux-foundation-easycla]

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 81.8%. Comparing base (66175c1) to head (bd886d0).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@          Coverage Diff          @@
##            main   #8140   +/-   ##
=====================================
  Coverage   81.8%   81.8%           
=====================================
  Files        194     194           
  Lines      13377   13377           
=====================================
  Hits       10951   10951           
  Misses      2029    2029           
  Partials     397     397           

Files with missing lines	Coverage Δ
instrumentation/net/http/otelhttp/client.go	66.6% <ø> (ø)

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[flc1125]

As mentioned in: #8131 (comment), we need to first mark it as deprecated before proceeding with the replacement. We need to give users a transition period.

I suggest that you discuss and confirm the specific details of the deprecation and replacement plan on the issue page so that we can proceed with the follow-up work.

PS: This issue is expected to be split into multiple phases for implementation.

[pellared]

From #8131 (comment):

I propose deprecating and later removing

Also #8140 (comment)

[pellared]

Please take a look at other "deprecation" PRs for reference such as #8117

[flc1125]

Blocked: Release plan