How old and how many miles (keystrokes) has your Mac done. Does seem to be a coincidence that the problem occurred after the upgrade. Most operating systems have a key repeat setting with a delay (sometimes configurable) and a repeat frequency (configurable) so that you only have to push a key once and hold it down, the setting is for all the keys including the space bar. I don't have Big Sur just yet but it's on the cards so I can't help here, but this key repeat setting is available on all Macs so I guess you could play around with it to confirm if it's a hardware issue.
My Mac is mid 2014 and only has average miles on it with no issues whatsoever (but doesn't run Big Sur yet).