[release-23.0] vtgate: fix handling of session variables on targeted connections (#19318)

[vitess-bot]

Description

This is a backport of #19318

[vitess-bot]

Hello @arthurschreiber, there are conflicts in this backport.

Please address them in order to merge this Pull Request. You can execute the snippet below to reset your branch and resolve the conflict manually.

Make sure you replace origin by the name of the vitessio/vitess remote

git fetch --all
gh pr checkout 19335
git reset --hard origin/release-23.0
git cherry-pick -m 1 0b345d26c8d2eea480291514de962e94dbc2e005

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 69.72%. Comparing base (7c76856) to head (33a7ba3).
⚠️ Report is 3 commits behind head on release-23.0.

Additional details and impacted files

@@               Coverage Diff                @@
##           release-23.0   #19335      +/-   ##
================================================
- Coverage         69.73%   69.72%   -0.02%     
================================================
  Files              1606     1606              
  Lines            214823   214818       -5     
================================================
- Hits             149798   149772      -26     
- Misses            65025    65046      +21     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 69.72%. Comparing base (7c76856) to head (33a7ba3).
⚠️ Report is 4 commits behind head on release-23.0.

Additional details and impacted files

@@               Coverage Diff                @@
##           release-23.0   #19335      +/-   ##
================================================
- Coverage         69.73%   69.72%   -0.02%     
================================================
  Files              1606     1606              
  Lines            214823   214818       -5     
================================================
- Hits             149798   149772      -26     
- Misses            65025    65046      +21     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.
• 📦 JS Bundle Analysis: Save yourself from yourself by tracking and limiting bundle sizes in JS merges.