jwz's favorite throbber (also my favorite) captured this feeling particularly well since it is literally an animated compass[1].
I actually got really into the history of browser throbbers back when I was in college — I ended up archiving all I could find from the mozilla ftp and internet archive[2].
[0]: https://www.jwz.org/doc/about-jwz.html
[1]: https://www.jwz.org/compass2.gif / https://www.jwz.org/doc/about-compass-anim.gif
[2]: http://cs.gettysburg.edu/~duncjo01/archive/browsers/throbber...
While I used to maintain an SeaMonkey (Mozilla Suite) xpfe complete theme with a properly animated throbber, I actually still use the jwz throbber through my unfinished xpfe userChrome.css in Firefox to this day.
Sadly, there are no css dynamic css classes above the #PanelUI-menu-button element in chrome://browser/content/browser.xhtml, so it's not possible to properly animate it without javascript; for now, it animates when you hover over it.
One weird side effect of this was that Internet Explorer and Explorer itself were integrated. At a time, you could set your desktop wallpaper to an HTML page. There were even "HTML apps" introduced around the same time* which I believe is still being somewhat continued today for Windows 10 widget development
I thought it was stupid and potentially dangerous because it misled users to treat the web and local resources equally, and put the same amount of trust in each. Of course nowadays, not treating local resources with the same amount of distrust we give the web is a major security fail, and that's why we must notarize and sandbox everything.
I liked throbbers because they signalled "ok, I'm going to the network to fetch what you asked for" as opposed to the hourglass cursor which indicated ordinary computer activity. It was Windows 98 that ruined the experience and thrill of "going to the network", because Microsoft decided that the web and the local desktop should merge into a single, seamless experience. They seemed not to understand that the network was fundamentally different, and in many ways more dangerous, than the local PC because it is almost always, as we say today, someone else's computer; and that the end user should be made aware of and encouraged to respect that difference.
I think the nostalgia for the feeling of navigating cyberspace is part of what inspires art movements like vaporwave, with its incorporation of 90s GUI elements in its aesthetic. In the 90s, there was always this ambient feeling of "this boxy beige Macintosh isn't a sleek Ono-Sendai cyberdeck, but it's an acceptable interim substitute until you get a cyberdeck which could be any day now". We were sort of roleplaying at being a part of sort of a beta version of Gibson's tragically hip cyberfuture, not realizing that we were ultimately being sold the shitty parts of that future without any of the cool parts. It's kind of like the joke about Bill Gates in hell: the cool stuff was just the demo.