router, backend: replace time.Time with mono-time to optimize duration calculation

[djshow832]

What problem does this PR solve?

Issue Number: ref #420

Problem Summary:
We're adding more and more metrics and the overhead of time.Now() is getting more.
time.Now() involves wall time and nanotime, but we only need nanotime to calculate duration.

What is changed and how it works:
Replace time.Time with monotime.Time.

Check List

Tests

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

Benchmark results:

BenchmarkGoNow
BenchmarkGoNow-8       	13206856	        82.03 ns/op
BenchmarkMonoNow
BenchmarkMonoNow-8     	33960902	        34.73 ns/op
BenchmarkGoSince
BenchmarkGoSince-8     	 9926468	       123.3 ns/op
BenchmarkMonoSince
BenchmarkMonoSince-8   	15168806	        66.29 ns/op

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.

Replace time.Time with mono-time to optimize duration calculation

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: xhebox

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-01-25 02:57:22.516275874 +0000 UTC m=+1015884.080573578: ☑️ agreed by xhebox.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

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Additional details and impacted files

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