Thanks to some help from a few friends, I got my iPhone back on my home WiFi network. It turns out what was happening was unrelated to the iPhone – my router had decided to stop giving it an IP address. This eventually started happening to other devices on my network as well. We swapped out the router (technically we moved the routing/DHCP server responsibilities to a different device), and everything started working as expected again.
Thanks to my colleague Laura for suggesting that it was likely the router causing trouble instead of my iPhone, and to my friend Joe for helping me confirm the issues and reconfigure the network.
I’m hoping this will be the last time I have to tinker with my home network setup in a long time.