I would say it is complicated, but also that Matrix is certainly open.

Technically Matrix and Element are independent and the specification is controlled by the Matrix Foundation and the "Spec Core Team". However there is significant overlap between people on the SCT and the foundation and Element employees. This is mostly because of history. At the start Matrix and Element were in most aspects the same people. Element was a company founded to make money with selling Matrix based products to then support the development of the Matrix protocol (I might be getting some of the details wrong, but I think that is roughly right). This resulted also in Element being one of the few Matrix employers early on, so people who ended up on the SCT were often either from Element or later hired by Element, because those people also wanted to work on Matrix as their day job instead of just in their free time.

More recently new SCT members were added, that aren't employed by Element (and there was at least one before that, who was never employed by Element), so Element's involvement in the SCT is clearly reducing. Similarly the SCT is supposed to make decisions, that don't benefit a single company (but of course that is hard to guarantee, so you need to judge that for yourself). I personally do believe, that every SCT member is trying to follow that rule.

Additionally the Matrix Foundation is currently in the process of setting up a more neutral governing board (it was already controlled by 5 guardians before, of which 3 were not involved directly with Element). You can read more about that setup here: https://matrix.org/foundation/governing-board-elections/ But the gist of that is that different sponsors as well as ecosystem and individual members can vote on representatives for the governing board and the governing board is then supposed to take over most governance responsibilities aside from the specification.

(For disclosure, I am both elected one of the elected board members as well as an employee of a different Matrix based company, but I am not speaking for either here.)

So I think there is clearly progress to make Matrix more independent of Element. It is also a fact that the Matrix Spec proposal process has always been open for anyone to submit a proposal, even if the SCT then sets the priorities on what gets merged into the spec. In my experience most of the proposals are stuck in the "needs more work" stage, which is something Element has historically put a lot of effort into and other companies and individuals either didn't want to put it the same effort or especially regarding the individuals, simply didn't have the resources to do that. But even that is getting more diverse nowadays.

There are also plenty of alternative clients for Matrix and a few alternative servers. They might not have the same polish as Elements products, but they do have a significant share of users, that are happy with them.

So I think Element is still very present in the Matrix ecosystem and that will still be the case for a while. But there is clearly work being done to make Matrix more independent and I think with the historical background it also makes sense why. There was a pretty good talk about that at the Matrix conference from kitsune about the mitosis of organisational structures.

Also, I don't think that few clients in the Matrix ecosystem support E2EE. I think most of the more popular ones support it nowadays: NeoChat, FluffyChat, Nheko, Fractal, gomuks, Cinny, Tammy, etc. It is actually quite hard to find a client, that doesn't support E2EE: https://matrix.org/ecosystem/clients/ (use the feature filter at the bottom to filter by E2EE support)

You can also read more about the foundation and how it is supposed to function here: https://matrix.org/foundation/about/
But to repeat my initial statement, I do think Matrix is independent in most aspects from Element, will become independent in most of the remaining aspects and that Element is currently simply a very large contributor and employer in the Matrix space, with a history without which we wouldn't have Matrix today.