ITEP-87135 API Test Rework & Reporting adjustments

[dpitulax]

📝 Description

Our current API tests print their results differently from the UI test suite.
UI tests always include a standardized result footer in the test logs, formatted as "NEX-Txxxxx: PASS/FAILED".
To improve consistency and make results easier to scan in logs and reports, we want API tests to produce the same footer format for each test ID.

What Was Changed

Added standardized footer reporting (NEX‑Txxxxx: PASS/FAIL) to API tests.
Replaced redundant class‑based API tests with plain pytest function tests.
Improved code readability and consistency across test files.
JIRA: ITEP-87135

✨ Type of Change

Select the type of change your PR introduces:

• 🐞 Bug fix – Non-breaking change which fixes an issue
• 🚀 New feature – Non-breaking change which adds functionality
• 🔨 Refactor – Non-breaking change which refactors the code base
• 💥 Breaking change – Changes that break existing functionality
• 📚 Documentation update
• 🔒 Security update
• 🧪 Tests
• 🚂 CI

🧪 Testing Scenarios

Describe how the changes were tested and how reviewers can test them too:

• ✅ Tested manually
• 🤖 Ran automated end-to-end tests

✅ Checklist

Before submitting the PR, ensure the following:

• 🔍 PR title is clear and descriptive
• 📝 For internal contributors: If applicable, include the JIRA ticket number (e.g., ITEP-123456) in the PR title. Do not include full URLs
• 💬 I have commented my code, especially in hard-to-understand areas
• 📄 I have made corresponding changes to the documentation
• ✅ I have added tests that prove my fix is effective or my feature works