scheduler: stop the running job when it has been balanced

[bufferflies]

What problem does this PR solve?

Issue Number: Close #9484

What is changed and how does it work?

Check List

Tests

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

Code changes

• Has the configuration change
• Has HTTP API interfaces changed (Don't forget to add the declarative for the new API)
• Has persistent data change

Side effects

Related changes

Release note

None.

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[Copilot]

Pull Request Overview

This PR adds a mechanism to stop a running balance-range job once the specified key ranges are deemed balanced.

• Introduce defaultBalancedThresholdRatio and isBalanced() logic to detect balanced ranges.
• Cache the computed plan in the scheduler to avoid redundant prepares and stop scheduling when balanced.
• Add new Prometheus metrics (scheduled, prepare-failed) and update unit tests for the balance check.

Reviewed Changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 2 comments.

File	Description
pkg/schedule/schedulers/metrics.go	Added balanceRangeScheduledCounter and balanceRangePrepareFailedCounter.
pkg/schedule/schedulers/balance_range.go	Introduced balanced-threshold logic, cached plan in scheduler, updated IsScheduleAllowed/Schedule.
pkg/schedule/schedulers/balance_range_test.go	Expanded test range and added assertions for the new isBalanced behavior.

Comments suppressed due to low confidence (1)

pkg/schedule/schedulers/balance_range.go:415

• Storing plan on the scheduler struct can introduce data races if IsScheduleAllowed and Schedule run concurrently. Consider passing the plan through method arguments or protecting access with a mutex.

		s.plan = plan

[Copilot]

Calculating maxScore and minScore from sources before sorting can yield incorrect values. Move the max/min computation after sorting or compute them by scanning scoreMap directly.

Suggested change

	maxScore := scoreMap[sources[0].GetID()]
	minScore := scoreMap[sources[len(sources)-1].GetID()]
	balancedThreshold := int64(float64(averageScore) * defaultBalancedThresholdRatio)
	if balancedThreshold < 2 {
	balancedThreshold = 2
	}

[Copilot]

When prepare fails in IsScheduleAllowed, the new balanceRangePrepareFailedCounter metric should be incremented to track these failures consistently.

Suggested change

	log.Warn("failed to prepare balance key range scheduler", errs.ZapError(err))
	log.Warn("failed to prepare balance key range scheduler", errs.ZapError(err))
	balanceRangePrepareFailedCounter.Inc()