[release-1.31] Rework loadbalancer server selection logic

[brandond]

Proposed Changes

• Backport Rework loadbalancer server selection logic #11329

Types of Changes

backport; tech debt; enhancement

Verification

See linked PR for verifiable changes

Testing

Linked Issues

• [release-1.31] loadbalancer improvements #11424

User-Facing Change

The embedded client loadbalancer that handles connectivity to control-plane elements has been extensively reworked for improved performance, reliability, and observability.

Further Comments

[codecov]

Codecov Report

Attention: Patch coverage is 79.50963% with 117 lines in your changes missing coverage. Please review.

Project coverage is 42.87%. Comparing base (d28a780) to head (d1aa856).
Report is 14 commits behind head on release-1.31.

Files with missing lines	Patch %	Lines
pkg/agent/loadbalancer/servers.go	83.81%	40 Missing and 5 partials ⚠️
pkg/etcd/etcdproxy.go	0.00%	19 Missing ⚠️
pkg/agent/loadbalancer/loadbalancer.go	74.50%	8 Missing and 5 partials ⚠️
pkg/agent/tunnel/tunnel.go	82.66%	10 Missing and 3 partials ⚠️
pkg/server/router.go	85.18%	5 Missing and 3 partials ⚠️
pkg/agent/loadbalancer/httpproxy.go	80.00%	5 Missing and 2 partials ⚠️
pkg/agent/config/config.go	63.63%	3 Missing and 1 partial ⚠️
pkg/util/client.go	66.66%	2 Missing and 1 partial ⚠️
pkg/agent/proxy/apiproxy.go	66.66%	1 Missing ⚠️
pkg/cli/token/token.go	0.00%	1 Missing ⚠️
... and 3 more

Additional details and impacted files

@@               Coverage Diff                @@
##           release-1.31   #11457      +/-   ##
================================================
- Coverage         47.21%   42.87%   -4.35%     
================================================
  Files               179      181       +2     
  Lines             18569    18752     +183     
================================================
- Hits               8767     8039     -728     
- Misses             8459     9524    +1065     
+ Partials           1343     1189     -154     

Flag	Coverage Δ
e2etests	35.07% <63.57%> (-7.23%)	⬇️
inttests	18.73% <20.84%> (-15.96%)	⬇️
unittests	14.30% <52.53%> (+0.44%)	⬆️

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