This is a very cool art project.

Is there a practical daily driver Linux that has this feel and vibe? Can I do this cleanly with GNOME/Debian or XFCE/Manjaro, or a bespoke OS with an underlying package manager?

The closest I know of is Blue95. I have only run the live environment but it worked pretty well and was impressive.

"Blue95 is a modern and lightweight desktop experience that is reminiscent of a bygone era of computing. Based on Fedora Atomic Xfce with the Chicago95 theme."

https://github.com/winblues/blue95

Depending on your chosen desktop and era, there are also things like TDE (trinity desktop environment) a fork (or spiritual successor) of the KDE 3.x environment: https://www.trinitydesktop.org/media/screenshots/large/tde3....

And if you like Gnome 2.x, there's MATE: https://mate-desktop.org/

https://github.com/grassmunk/Chicago95 and https://github.com/B00merang-Project/Windows-95 get quite close if you use them together. The B00merang one has presets for the GNOME/Cinnamon/MATE desktop and a GTK+4 theme (which adds terrible padding compared to the usual GTK+3 one, but at least it has visible and properly 3d-shaded widgets).

Most window managers will have a theme that looks like the old 90s. They're commonly named things like "Chicago," or "Redmond."

fvwm95, or newer: https://github.com/jcs/progman

I'd love a similar compositor for Wayland.