tests: Fix unstable schema test (#8972)

[ti-chi-bot]

This is an automated cherry-pick of #8972

What problem does this PR solve?

Issue Number: close #8968, close #8911

Problem Summary:
#8955 introduced a check on the cache gc_safepoint is not updated, but the background task of DDL sync make the ut unstable

What is changed and how it works?

• Disable the background task when profiles.default.ddl_sync_interval_seconds == 0
• Refine the code in TiDBSchemaManager.h with comments on locking schema_syncers_mutex
• Refine the code in SchemaSyncTest to use temporary instance instead of the instance in global_context

Check List

Tests

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

Side effects

• Performance regression: Consumes more CPU
• Performance regression: Consumes more Memory
• Breaking backward compatibility

Documentation

• Affects user behaviors
• Contains syntax changes
• Contains variable changes
• Contains experimental features
• Changes MySQL compatibility

Release note

None

[JaySon-Huang]

/run-all-tests

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: JaySon-Huang, Lloyd-Pottiger

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• OWNERS [JaySon-Huang,Lloyd-Pottiger]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-05-07 08:29:16.364764262 +0000 UTC m=+950710.121899830: ☑️ agreed by JaySon-Huang.
• 2024-05-07 08:51:55.283254753 +0000 UTC m=+952069.040390323: ☑️ agreed by Lloyd-Pottiger.