I used to manage on of those QA teams, test teams and also a testing center of excellence for a while.
The test center of excellence did not a bad job, aligning global practices, sorting training and that guidance and development side, it had a fairly clear testing remit.
The QA team less so as none of the developers, designers or project managers reported to me so I had very little authority to change quality, I experimented in servant leader to these groups but really ended up back as test manager and not QA. Note I that I have been both developer and a senior project manager which gave me a better chance of QA influence but still it was a bit of an odd role.
I do not manage people any more and from my experience the separation of the team was less effective than being embedded in teams. I do though still dual role as a coach and now and again I help teams get up and running with quality planning activities including those other roles.
I am fine reporting into engineering managers and multiple PM’s on any given day on the work activities. The development of the testing craft though does need a different model, we went the testing guild option, mainly for testers but we also had others, this is where a lot of the skill development, guidance and practice shifted to rather than from the manager. This works well in my view, on balance better than the separate team managers for QA or testing.
There is a risk the testing craft gets diminished by not having a person of influence on your side, be the person of influence if you need to, set up monthly knowledge and guidance sessions focused on QA or testing, make sure others have access to this group, invite other roles so they understand your value better.
The engineering manager approach can have other benefits like better understanding of other roles and picking up new skills beyond your primary area.
There is an argument on independent testing, I tend to take the view I can change hats and create a distance from the build that lowers that risk though and make a judgement if I think that is threatened and call a friend.
Anyway test guild of some sort is likely what you need in that model so it does have a vehicle for focusing on your craft whether its QA or testing or something else, we have mobile development and design groups as well so this is not just important for testing.