mcs: fix potential data race in scheduling server (#8539)

[ti-chi-bot]

This is an automated cherry-pick of #8539

What problem does this PR solve?

Issue Number: Close #8538

What is changed and how does it work?

Check List

Tests

• Unit test
• Manual test (add detailed scripts or steps below)

for i in {1..100}; do
	go clean -testcache
	go test -timeout 120s -run ^TestAPI$ github.com/tikv/pd/tests/integrations/mcs/scheduling -race
done

Release note

None.

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: bufferflies, rleungx

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-12-11 10:09:14.627402878 +0000 UTC m=+433144.716205420: ☑️ agreed by rleungx.
• 2024-12-12 02:47:27.927129254 +0000 UTC m=+493038.015931796: ☑️ agreed by bufferflies.

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