cherry-pick #7523 to v1.66.x branch

[dfawley]

RELEASE NOTES: none

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 81.92%. Comparing base (35e915e) to head (9078b14).
Report is 1 commits behind head on v1.66.x.

Additional details and impacted files

@@             Coverage Diff             @@
##           v1.66.x    #7547      +/-   ##
===========================================
- Coverage    81.93%   81.92%   -0.01%     
===========================================
  Files          360      360              
  Lines        27539    27542       +3     
===========================================
  Hits         22565    22565              
  Misses        3785     3785              
- Partials      1189     1192       +3     

Files	Coverage Δ
balancer_wrapper.go	86.62% <100.00%> (-0.22%)	⬇️
clientconn.go	93.09% <100.00%> (-0.02%)	⬇️

... and 10 files with indirect coverage changes