[18.5] Fix test failure by adjusting dates to match partition range

What does this MR do and why?

This backports !211190 (merged) to 18-5-stable-ee because we have seen pipeline failures as well.

Related: https://gitlab.com/gitlab-org/quality/test-failure-issues/-/issues/12725+

The test was failing because it tried to insert a record with date '2025-07-15', which is before the partition range(starts August 1, 2025). When the sync trigger tried to copy this to the partitioned table, it failed because no July partition exists. This MR fixes the test by:

• Changing test data to use dates within the August partition range (starting from 2025-08-01)
• Overriding START_DATE to 2025-08-10 in the test context to verify the exclusion logic
• Ensuring the migration correctly identifies min_id for records on or after START_DATE

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• This MR is backporting a bug fix, documentation update, or spec fix, previously merged in the default branch.
• The MR that fixed the bug on the default branch has been deployed to GitLab.com (not applicable for documentation or spec changes).
• The MR title is descriptive (e.g. "Backport of 'title of default branch MR'"). This is important, since the title will be copied to the patch blog post.
• Required labels have been applied to this merge request
  • severity label and bug subtype labels (if applicable)
  • If this MR fixes a bug that affects customers, the customer label has been applied.
• This MR has been approved by a maintainer (only one approval is required).
• Ensure the e2e:test-on-omnibus-ee job has succeeded, or if it has failed, investigate the failures. If you determine the failures are unrelated, you may proceed. If you need assistance investigating, reach out to a Software Engineer in Test in #s_developer_experience.

Note to the merge request author and maintainer

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• Once the backport has been merged, the commit changes will be automatically deployed to a release environment that can be used for manual validation. See after merging runbook for details.