Chicken and egg
Any sort of document-based app benefits tremendously from tabs, and thus it would be unfortunate to have to lose that feature when making it a Web App. I for example often need a couple Google Docs open at once. I would very much like to have Google Docs as a separate item in my Dock though. However, I don't want to be forced to have each individual Google Document in a separate window like it's Mac OS 9 just because it's a "Web App".
Or for example Airtable. I have a few Airtables that I basically always have open. I currently have them "pinned" just because if not they become impossible to find in the sea of other windows and tabs in my browser. I would love to command-tab to Airtable and bring these up, but not have them in an overlapping mess of windows.
Another great example is social media "Web Apps" (like Elk for Mastodon), which basically get "stacks" for free by leveraging tabs. Instead of the Elk team having to develop an "internal tabbing" feature, I can just have a tab for each hashtag I am following. But this does not mean that I want all these tabs mixed in with random other unrelated websites.
Literally any app (vs. "page") that uses multiple windows that you would personally prefer to group into tabs is a good candidate. Tabs are a window organizational tool, they have no inherent "webness" to them aside from that being the first place they originated. macOS's AppKit framework has built-in support for automatically making document-based apps support tabs with zero additional programming. I assure you this feature wasn't added in to allow anyone to write a web browser. In fact, I think the opposite of your assertion is true: the more like an "app" the thing you're turning into a Web App is, the more likely it is to use multiple windows, and thus the more it can benefit from tabs. I agree that if you are for some strange reason turning a blog into a Web App, then tabs don't make any sense, but it also doesn't make sense to turn it into a Web App.
I agree that it would be much nicer to have this at the system level.
"A web application (or web app) is application software that is accessed using a web browser. Web applications are delivered on the World Wide Web to users with an active network connection."
It works in Firefox, not sure why Wikipedia has that wrong.
Under the Window menu there are options to Show Previous Tab, Show Next Tab, and Move Tab to New Window, but they’re all greyed out.
Like when I use Google Docs, I've usually got several open as separate tabs in my browser. If I wanted Docs as a webapp, it wouldn't have the tabs functionality anymore, which would make it immediately useless. In the way that every IDE or Photoshop now use tabs inside the app.
We're at this place now where I actually wish tabs weren't handled by applications but rather by the OS, together with windows. Let me create a window that has three Chrome tabs, a Safari tab, a Terminal tab, and a Preview tab. Another window with a Word (installed) doc tab, an image in Photoshop tab, and several Finder tabs.
The fact that web apps can't be tabbed is almost this weird step backwards.