server/cluster: avoid repeated region size scans (#11072)

[ti-chi-bot]

This is an automated cherry-pick of #11072

What problem does this PR solve?

When multiple stores are in the Preparing state, PD recalculates the same
region sizes for every store during each checkStores round. With placement
rules enabled, calculateRange also calls GetRegionSizeByRange once for
every matching rule.

For non-empty key ranges, these repeated scans can significantly increase
Region tree lock contention and delay Region heartbeat processing.

Issue Number: ref #9574

What is changed and how does it work?

Cache region sizes by key range within one checkStores round so all Preparing
stores reuse the same calculation.

Load each range size before processing its matching placement rules instead of
scanning the range once per rule.

Discard the cache after every `checkStores` round so the next round reloads
region sizes from the current Region tree.

Limitations

This PR eliminates duplicate range scans across placement rules and Preparing
stores within one checkStores round. Each unique non-empty range is still
scanned in O(N) time once per round. Supporting O(log N) range queries or
incremental range-size aggregation will be handled separately.

Check List

Tests

• Unit test

Related changes

• core: return the region tree size if scan all the regions #9580 optimizes the full key-range lookup.
• Need to cherry-pick to the release branch.

Release note

Reduce repeated Region tree scans when multiple stores are preparing.

Summary by CodeRabbit

• Bug Fixes

  • Improved store readiness and placement-rule threshold calculations by reusing region-size results within each calculation round.
  • Corrected placement-rule range evaluation to begin with the first rule matching the target store.
  • Preserved separate calculations across rounds to prevent stale sizing results.

• Tests

  • Added coverage for cache reuse across stores and placement rules, independent range caching, and calculation-round isolation.

[ti-chi-bot]

This cherry pick PR is for a release branch and has not yet been approved by triage owners.
Adding the do-not-merge/cherry-pick-not-approved label.

To merge this cherry pick:

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[ti-chi-bot]

@lhy1024 This PR has conflicts, I have hold it.
Please resolve them or ask others to resolve them, then comment /unhold to remove the hold label.

[ti-chi-bot]

@ti-chi-bot: ## If you want to know how to resolve it, please read the guide in TiDB Dev Guide.

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[ti-chi-bot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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[ti-chi-bot]

Cherry-pick conflicts appear resolved; removing the do-not-merge/hold label.