Apple - Can the spacing of menu bar apps be modified in Big Sur?

Actually, there appears to be some way to do this, since the newest version of Bartender allows you to change or remove spacing in the menu bar. The app is free in beta (and, accordingly, still has a few wrinkles still to be ironed out) and will cost $15 once the final version is released.

To change the spacing with Bartender, install the app, open the preferences window, and under "General" change "Menu bar item spacing" to "Small Spacing." After logging out and back in (or, if that doesn’t work, rebooting), the changes should take effect.

It is the approach Apple is taking, getting the menu bar items wider. Some conspiracy theories are stating that it might be the beginning of touch screen macs since the new UI is a lot more touch friendly. You can watch "Snazzy Labs" video about it while Big Sur was in beta. I believer it was called "Big Sur's Secret" or smt...

Back to your question, no. At this point, until a developer gets his hands on a 3rd party app or apple listens to its customers resisting the change, you cannot change any of the Big Sur spacings.

Addition: At the time of writing this answer, there were no software capable of doing such thing. However, as the answer above me mentioned a newer version of "Bartender" capable of such thing. This answer is obsolete.