Might also be good to remember, that even modern orgs separate Ops from devops. It’s going to depend on how fast or how mature the product is. Many orgs separate security out into a team, but even when they do, we all own security.
All testing is part of the SDLC, Which means that even if Ops is a separate team, the customer-feedback part of the SDLC has to be fed directly back into the team that builds the software. The only time a test team “owns” testing of any kind is in an org where QA is a business process and not a hygiene thing. Lots of companies still work that way, but much like when you ask who owns security? The answer needs to be, everyone. The further you go into mature service industries, the more you will see separation of ownership, but even in the same company, teams that innovate will take ownership in order to iterate faster. BUT.
To answer your question, whoever releases code to the customer, has to be a stakeholder in the testing, and thus in the E2E. It’s not for us as testers to decide this stuff, if your company releases multiple products, that’s multiple stakeholders, and I think that’s the reason some companies create siloed QA teams. They have multiple related products, and don’t want the company image to get hurt by one bad apple, so they create a guardian team and happen to call it QA. One possible route may be to create better communications between teams. You could go and ask the Amazons and Microsoft’s of this world, and still get different answers. I suspect it’s the biggest money earner product-team that may decide, I would be trying to get a transfer to that org.