I also think the taskbar showing only icons is confusing when we have the same app opened multiple time. I have a similar organization as you for work: a Firefox window on desktop 10 for Calendar, Mail, another on desktop 9 for company Chat, another (main) window on desktop 1, another on desktop 2 for a different project, ... By default on Gnome they would be all grouped into 1 Firefox icon. We can change the settings to not group apps, but a bunch of Firefox icons next to each others doesn't help either.

I recently discovered in the Fluxbox edition of MX Linux the taskbar Tint2. It was configured in a way that split the taskbar into dedicated and fixed workspace areas. It's an efficient way to see quickly what app is on which desktop, and clicking on one app will bring me to the desktop where the app is. I can also move apps to different desktop with the mouse by dragging them in the bar (for instance drag terminal of desktop 2 in desktop 3 next to the file browser opened there).

It looks like this: https://imgur.com/a/FGNfL7e

I currently use this taskbar with Openbox, but it should work with other DE/WMs. It has some bugs in some edge-cases so it's not perfect, but I like the concept.

I went on a quest to configure the same behavior on different DEs. I couldn't reproduce it with the default bars of Budgie, Cinamon, Gnome, Mate. KDE was the only one where I was close to achieve this. In the default KDE bar, it's possible to sort the apps by their workspaces. But it only sorts them, it doesn't split clearly by static desktops like you can do in Tint2. Still, KDE showed once again it was one of the most customizable :)