Update bundle script and workflow for NPM 12 changes

[t1m0thyj]

What It Does

Ports feedback from PR #2876 to the V3 branch

How to Test

Review Checklist
I certify that I have:

• updated the changelog
• manually tested my changes
• added/updated automated unit/integration tests
• created/ran system tests (provide build number if applicable)
• followed the contribution guidelines

Additional Comments

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.16%. Comparing base (023fa2a) to head (d50859a).

Additional details and impacted files

@@           Coverage Diff            @@
##           master    #2884    +/-   ##
========================================
  Coverage   92.16%   92.16%            
========================================
  Files         657      657            
  Lines       20572    20572            
  Branches     4684     4555   -129     
========================================
  Hits        18961    18961            
  Misses       1607     1607            
  Partials        4        4            

☔ View full report in Codecov by Harness.
📢 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.

[github-actions]

Client artifacts:

• CLI: https://github.com/zowe/zowe-cli/actions/runs/33926805998/artifacts/9957562546

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud