If I connected a LAN cable to my PC so that I could get a better PING in Fortnite, would that worsen the Wi-Fi of the others in the household?
Only when he is overloaded the server from the provider.
Yes and no. Usually everyone gets the same share of the available bandwidth of the Internet connection, regardless of whether the device is connected via LAN or WLAN. Of course, this is limited by the transmission speed to the respective device.
If you now use more bandwidth or connect an additional device, the LAN and WLAN will be slower for the others. But this is not the case in your case.
A bit like how a ferrari worsens the autobahn compared to a golf…
that is to say, if you are all on the same network and share an internet connection, then the internet "worsens" for everyone to the same extent. But that has no influence on whether lan or wlan.
with the lan you have the advantage that the connection is more direct. I.e. If you let your warrior attack, it won't take that long before he does this on the server. (ping) but that has no influence on the internet of the others.