Backport/budgets projects searchable

[BarbaraOliveira13]

🎩 Description

Backport #12017 fix:projects displayed in search when not published

📌 Related Issues

Link your PR to an issue

• Related to #12017
• Related to #11721
• Notion card

Testing

1. Duplicate a seed process (unpublished)
2. Go to new process components
3. Create a budget
4. Create a project
5. In private browsing, see that the project is displayed in search for visitors, even though the process and the budget component are unpublished

Tasks

• Add specs
• Add note about overrides in OVERLOADS.md
• In case of new dependencies or version bump, update related documentation

📷 Screenshots

Please add screenshots of the changes you're proposing if related to the UI

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 89.11%. Comparing base (bd14241) to head (ea19cfd).
Report is 2 commits behind head on develop.

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #521      +/-   ##
===========================================
- Coverage    89.51%   89.11%   -0.41%     
===========================================
  Files           68       68              
  Lines         1622     1626       +4     
===========================================
- Hits          1452     1449       -3     
- Misses         170      177       +7     

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[Quentinchampenois]

CI is failing because of CodeCov upload, will be fixed in another PR