There is a difference between web sites and web apps.
There used to be time when we were actually taught in school that "web is not apps", so UI patterns don't necessarily apply: it's one page at a time, there's statelessness, reloads, so we should've looked at them as something special. That's the reason devs didn't really try to make their sites look and behave like apps - they were something else, on a different shelf.
These days we mostly look at web apps the same way as we look at "proper" apps. Web apps are almost proper apps now and users think less and less about technology behind the app, they use either and expect them to behave similarly. An app is an app. So we should be free to apply whatever UX pattern works on desktop and mobile apps to web apps.
Would you call Facebook, Insta or X "websites"? What about web version of Word? I mean, my mom wouldn't be able to say it's a web app if I'd have shown her this screenshot:

While it's true that on mobile platforms we've almost lost this affordance (they still do use other affordances for similar stuff), macOS users still do expect ellipses on buttons that open another window (users do see modals as windows, for example), view or an app.
Append a trailing ellipsis to the title when a push button opens another window, view, or app. Throughout the system, an ellipsis in a control title signals that people can provide additional input. For example, the Edit buttons in the AutoFill pane of Safari Settings include ellipses because they open other views that let people modify autofill values.
The same goes for older Windows users
Proper use of ellipses is important to indicate that users can make further choices before performing the action, or even cancel the action entirely. The visual cue offered by an ellipsis allows users to explore your software without fear.
And newer Windows guidelines push heavily on it being as familiar to the older users as possible:
Windows 11 balances a new, refreshed look and feel with the familiarity of the Windows I already know. There is no learning curve; I can pick it up and go.
Web is cross platform, users come from different OSes, different devices, different form factors. So it's always a problem, which guidelines to use?
To answer that, we should answer these:
- Where do users come from? Is their environment using the patterns you're considering? Jakob's law is very important!
- What do users expect? Do they look at your web app as an app or as a web site? Do they expect it to work like their desktop apps do?
I have a personal anecdote about ellipses. It turned out that I have never paid any attention to them before I've learned about their purpose and whoever I asked were always shocked - they haven't noticed them either (and they're professional developers for websites... which could lead us to the answer about why you don't see them in web). And then i found a couple users that were using them a lot. Like almost relying on that affordance and feeling incredibly confused when a button or a menu item opened new window but didn't have an ellipsis in the label.
Remember that if you don't think it's significant, it doesn't mean your users agree. If you can help smaller group of users without making it worse to the majority of users, you should do it. It's always about your users.