Feature query interaction latency observability

[baiyuqing]

What problem does this PR solve?

Issue Number: close #xxx

Problem Summary:

What is changed and how it works:

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No code

Notable changes

• Has configuration change
• Has HTTP API interfaces change
• Has tiproxyctl change
• Other user behavior changes

Release note

Please refer to Release Notes Language Style Guide to write a quality release note.

None

[ti-chi-bot]

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[codecov-commenter]

Codecov Report

❌ Patch coverage is 84.50363% with 64 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (serverless@b0716f5). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
pkg/proxy/backend/cmd_processor_exec.go	84.29%	14 Missing and 5 partials ⚠️
pkg/proxy/backend/metrics.go	82.60%	8 Missing and 4 partials ⚠️
pkg/metrics/metrics.go	9.09%	10 Missing ⚠️
pkg/proxy/backend/sql_type.go	88.31%	6 Missing and 3 partials ⚠️
cmd/tiproxy/main.go	82.85%	6 Missing ⚠️
lib/config/proxy.go	79.16%	4 Missing and 1 partial ⚠️
pkg/metrics/interaction.go	96.07%	1 Missing and 1 partial ⚠️
pkg/proxy/backend/backend_conn_mgr.go	87.50%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@              Coverage Diff              @@
##             serverless    #1081   +/-   ##
=============================================
  Coverage              ?   56.74%           
=============================================
  Files                 ?       83           
  Lines                 ?     7528           
  Branches              ?        0           
=============================================
  Hits                  ?     4272           
  Misses                ?     2925           
  Partials              ?      331           

Flag	Coverage Δ
unit	56.74% <84.50%> (?)

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[ti-chi-bot]

@baiyuqing: The following test failed, say /retest to rerun all failed tests or /retest-required to rerun all mandatory failed tests:

Test name	Commit	Details	Required	Rerun command
pull-check	7b6a5b8	link	true	/test pull-check

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