Coming back to this some time after my original comment, a few more thoughts in no particular order:
> a modern, desktop-like UI that meets today's needs
What are "today's needs"? Why does the standard desktop interaction paradigm not work with them? Why does "move it into the browser" solve the problem?
> it actually has some useful features to help with your browsing management
I can see some potentially-interesting features in the demo GIFs, but they don't make it clear why I'd want them through a desktop-style interface. Why not as just a browser extension or similar? What does the desktop paradigm provide that's a meaningful enhancement for the end user and not just a tech showcase?
> And then a "revolutionary" product comes out that puts our links & tabs collapsed on the side, with some extra features. Magical, right :)?
It's a bit overdone, sure. I won't disagree with that. But why does it keep happening?
imho it happens because the standard tab setup of "put all the tabs at the top of the window" had obvious shortcomings for a meaningful-enough group of users, and moving it to the side -- be that as a list, a tree, ... -- had benefits that those users appreciated, and that the more-average user may also find benefit in. Tabbed browsing had a significant benefit over the traditional windowed browsing, and imho it seems that moving them to the side has enough of a benefit over the "standard" one-row top-only tabs that people are moving to it.
But what does the desktop paradigm then offer over that? From my quick experimentation, I couldn't even figure out how to get value out of the base UI; this discourages me from then wanting to then try to ex. install your browser extension.
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Who's the intended user? Is it specifically for desktop-heavy power users? Is it for less-technical users to gain a better interface for browser interaction?
Why floating window management? With a surprising amount of people's interactions with the web moving to mobile (smartphones, tablets), I could see the floating window interactions actually being a drawback. Tiling windows might be better, but again that's potentially very user-dependent.
Jumping off of the floating window question, where is the intended use-case? Is this for desktop users? Are tablets a supported use-case? Smartphones? Where's the line drawn? If you intend to support more than the desktop user, how will you handle the lack of precise touch? The current UI has annoyingly-small icons on desktop; if mobile is an intended use-case I could see this very quickly becoming infuriating.
How is accessibility handled? Is keyboard-only interaction possible? What about screen readers? As a disabled person, I'm pretty tired of seeing user interfaces that are incredibly unfriendly to me because they rely on precise click/tap targets that I struggle immensely to properly use at times.
The product might benefit from having an actual tour / demo / etc. It's very unclear what the true use-case for it is. Every major (desktop) OS already has drag-and-drop, multiple workspaces, floating windows, ... Having some kind of walk-through would probably go a long way towards helping people understand.
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I don't say these things to discourage you, but this just doesn't feel ready for release yet. The sheer number of comments here on HN expressing negativity about this, at least to me, signal that the product's use-case isn't clear and that it's not obvious why this would be wanted. As a tech person, I very well understand the desire to make cool tech and show it off, but cool tech does not a product make. This reads as a tech demo being dressed up as a product, which explains a lot of the negativity here.
Your comment below[0] makes it a lot more clear that this is less "real serious product" and more "toy/tech demo/similar," and if it had been expressed as such from the start, I think the reception would have been better.
Hopefully these thoughts are of use! I do love seeing experimentation outside of the standard ways of interacting with things, and I think that with more refinement and experimentation you might find something interesting with this idea.
[0] https://news.ycombinator.com/item?id=41872816