Should Safari be doing stuff during Power Nap?

When I’m not using it, my 2014 MBP sits plugged in, on my desk, where I use my Mini. Recently, I’ve noticed that when FaceBook makes a ‘ping’ notification in Safari on my Mini, I also get a ping coming out of the laptop.

The laptop is running 10.15.5. Apple’s support page about Power Nap: https://support.apple.com/en-gb/HT204032 says nothing about Safari, but does say "During Power Nap, your Mac plays no system sounds". I suppose it’s arguable whether noises from Safari are ‘system’ sounds.

I dare say that ‘this is how it is’, but I’m surprised I’ve never noticed it before. Does this mean that any AJAX-type webpage could be set-up to run while the computer is napping?

Or is my computer not actually napping at all?