If I had to take a wild shot in the dark my best guess is that your router’s upstream connection settings are a bit messed up and whenever your ISP gives you a new ip dhcp is taking a long time for whatever reason. You could try to pay attention to if your outgoing ip changes whenever this happens https://www.showmyip.com/
I guess also I’m assuming you’re using a router with a built-in either cable or fiber modem? If you have a separate modem you might want to see about resetting it as well.
I wonder if it’s going to make installing the initial f-droid apk a huge pain though. Since normally you need to just download it in your browser and install it.