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)

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[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

[MrAlias]

There is not now way to set the client used by Get, Post, PostForm, and Head without using this deprecated value. An alternative should have been explored or those methods also handled in this process.