It should be under engineering but as a seperate skill/role. To ship fast you want QA aligned with milestones, sprints etc. You want QA to feel the deadlines, and then like an Eng push up if things aren't realistic.

What I have seen before with QA is a queue like system. Hand to QA. get back in 3 days. Not the QA persons fault. It is the setup if the org that is wrong.

Imagine if you had a code review role and code review team and you had to wait to get your code OKed. We wouldn't put up with it.

QA teams seperate from Eng worked when the software was burned to CD rather than uploaded to s3.