If you're having insane issues with Safari in Big Sur just... pausing... for... several... seconds... repeatedly... and it's about to drive you insane, go grab the Safari Technology Preview:
https://developer.apple.com/safari/technology-preview/
Turns out there is a horrible bug in the 14.1 builds that causes every database access to fail the first time, after a full timeout.
Second attempt works.
STP (build 126, 14.2) fixes this. When Safari is officially updated to 14.2, it should no longer exhibit this problem, but if, like me, you're about to lose your freaking MIND, go grab STP.
(And then tell me how you like the new tab UI... not sold...)