HSR is the easiest example of rasterizing Flash content being a bad idea, because there is just so much content. Even just the Sbemails compilation (1-200) is 10 hours, and for a DVD-quality video (480p) that's almost double the size of the HSR collection that I have (2000-2009 from archive org).

The site does work via Ruffle (even the menus, though some links seem broken) and they still make new ones (sbemail-210-robots, backtoawebsite) with Flash versions. There is also an old.homestarrunner so you could probably run this with a browser that still runs Flash, lacking one I'm not sure the exact URL to do so via standalone or even if the links will properly work there.

Local is still probably best, though still a mess with so many SWFs.

Homestar Runner's website still works through the use of Ruffle, an open-source and secure Flash reimplementation. The loss of the easter eggs is a big drawback, but on the other hand it does mean that you focus more on the content than constantly looking for things to click on.