ci: Temporarily disable warehouse testing of private tasks

[KKould]

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Summary

track: #18706

ci test-private-task recently encountered a warehouse test exception, which cannot be reproduced locally. Temporarily shut down the warehouse test.

Tests

• Unit Test
• Logic Test
• Benchmark Test
• No Test - Explain why

Type of change

• Bug Fix (non-breaking change which fixes an issue)
• New Feature (non-breaking change which adds functionality)
• Breaking Change (fix or feature that could cause existing functionality not to work as expected)
• Documentation Update
• Refactoring
• Performance Improvement
• Other (please describe):

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This change is