Fix error contain checks in vtgate package

[GuptaManan100]

Description

We were using some anti-patterns in the testing code for vtgate package like -

assert.Contains(t, err.Error(), ...)

instead we should be using

assert.ErrorContains(t, err, ....)

This PR fixes these anti-patterns.

This PR is the first change needed to fix the failing tests as seen in https://github.com/vitessio/vitess/actions/runs/10488116666/job/29052695413?pr=16619. The idea is to fix these anti-patterns, and then while running upgrade downgrade tests, we ignore assert.ErrorContains type of checks because we don't need to guarantee that the error messages don't change across version upgrades.

This is also the reason this PR needs to be backported to release-20.

Related Issue(s)

Checklist

• "Backport to:" labels have been added if this change should be back-ported to release branches
• If this change is to be back-ported to previous releases, a justification is included in the PR description
• Tests were added or are not required
• Did the new or modified tests pass consistently locally and on CI?
• Documentation was added or is not required

Deployment Notes

[vitess-bot]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 68.90%. Comparing base (a54d5ec) to head (5992f48).
Report is 12 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #16672      +/-   ##
==========================================
- Coverage   68.93%   68.90%   -0.03%     
==========================================
  Files        1562     1562              
  Lines      200767   200941     +174     
==========================================
+ Hits       138407   138468      +61     
- Misses      62360    62473     +113     

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