This does remind me a bit of a personal knowledge management solution that has (fairly) recently gone out of beta, AnyType [0], as that too was sometimes referred to as an "operating system for the new internet" and received similarly skeptical reception. Seen them refine the concept into a more rounded project, since the closed alpha, that has been rather successful in the PKM space, though the end product never fully fit my personal use cases.
From previous projects [1] (during which I merely made some minor modifications to a pre-existing FOSS project and took a look at the code of different "web-desktops" codebases), I get how much goes on under the hood of any desktop-like interface running in JS, so seeing one that also integrates handling the tabs of the "host browser" is immensely impressive, though of course I understand those highlighting the inefficiencies such an approach can bring.
I very much appreciate the appearance, especially the subtle use of glass like transparency on window borders and the way third-parties like Soundcloud seem to be embedded.
I will have to agree with some commenters that perhaps the privacy promise should be made more clear as to what the current state is. I understand that implementation takes time, but to build trust, being as transparent as possible from the start is invaluable.
Furthermore, I see potential for this project, perhaps with a bit of tunnel vision due to me being immersed in the space, in the PKM field, as there, despite web-first applications being the norm, there is still a hole that I feel could be filled concerning making open tabs as part of an active project directly accessible and manageable, rather than needing to import web pages, then switch to the application, as is the case with most current solutions like MyMind [2]. Especially, as there must be people other than myself whose PKM does necessitate actively using roughly 100 tabs at a time...
Additionally, if I may, perhaps the potential would have become more clear to some on here if you had linked the learn section [3] in your original post. It doesn't appear accessible on the homepage either, which is a shame, because that gave me a far better idea of the project in its entirety. Especially the search implementation showcased there has potential depending on the execution and should, in my opinion, be something you highlight on the homepage too.
Lastly, I want to mention that you are doing a great job taking the occasionally a bit harsh, but generally fair reaction the HN crowd can have to showcases on the chin. That takes maturity and professionalism, especially on a passion project.
[0] https://anytype.io/
[1] https://ethical-ai.eu/
[2] https://mymind.com/
[3] https://savaos.com/learn