[release-3.6] Semi-Automated cherry pick of #20017 (was Update go.opentelemetry.io/contrib/instrumentation/google.golang.org/grpc/otelgrpc to work with v0.61.0)

[dims]

Modified version of #20017 suitable for 3.6 branch.

Do not update to otelgrpc v0.61.0 here, just drop the usage of the deprecated APIs (deprecated earlier but dropped in v0.61.0)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 68.92%. Comparing base (7b35142) to head (5baf45e).
Report is 5 commits behind head on release-3.6.

Additional details and impacted files

Files with missing lines	Coverage Δ
server/etcdserver/api/v3rpc/grpc.go	95.00% <100.00%> (-0.13%)	⬇️

... and 19 files with indirect coverage changes

@@               Coverage Diff               @@
##           release-3.6   #20043      +/-   ##
===============================================
+ Coverage        68.88%   68.92%   +0.03%     
===============================================
  Files              420      420              
  Lines            35613    35612       -1     
===============================================
+ Hits             24531    24544      +13     
+ Misses            9652     9638      -14     
  Partials          1430     1430              

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[dims]

/assign @ahrtr

if this lands, happy to do another PR for changelog as well.

[ahrtr]

LGTM & thx

cc @fuweid @ivanvc @jmhbnz @serathius

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[ivanvc]

/retitle [release-3.6] Semi-Automated cherry pick of #20017 (was Update go.opentelemetry.io/contrib/instrumentation/google.golang.org/grpc/otelgrpc to work with v0.61.0)