I've worked with various types of QA teams over the years (all in SaaS). Based on my experience, from MOST effective to LEAST effective:
1. QA team works on test harnesses, automation, and works alongside developers to improve how we do testing. This was by far the most effective.
2. No QA team. Developers own every aspect of quality. This worked, but was not as effective as #1.
3. All releases are thrown over the wall to QA who stamp them and do the deploys. This shifted the responsibility for quality to people who weren't as familiar with the code and weren't equipped to fix it. Outages abound. It also slowed releases to a crawl.
4. QAs are non-technical. They mostly write and manage test cases. It's up to the developers to implement tests, but some tests are done manually by QA. I never saw any benefits from tracking test cases outside of the code that validates them. Properly prioritized tickets were fine for defect follow-up. Manual testing might be ok if you're a new startup, but it quickly becomes untenable as you grow.