SNOW-1691909: Move short regress tests to precommit

[sfc-gh-lmukhopadhyay]

1. Which Jira issue is this PR addressing? Make sure that there is an accompanying issue to your PR.

   Fixes SNOW-1691909

2. Fill out the following pre-review checklist:

   • I am adding a new automated test(s) to verify correctness of my new code
     • If this test skips Local Testing mode, I'm requesting review from @snowflakedb/local-testing
   • I am adding new logging messages
   • I am adding a new telemetry message
   • I am adding new credentials
   • I am adding a new dependency
   • If this is a new feature/behavior, I'm adding the Local Testing parity changes.

3. Please describe how your code solves the related issue.

   Please write a short description of how your code change solves the related issue.