I haven’t seen this happen for a while now, either with just Ethernet, just Wi-Fi, or both. I couldn’t say which update to which package fixed the issue, but it does seem to be fixed now either way, at least for me.
I’m experiencing this as well under fedora 39 with gnome. I’d say the check would make sense if it was headless. Having a popup flash on the screen each time internet connectivity is checked is a tad annoying tbh.