the phone part would the tricky bit. i think it should be doable using Termux on Android to run it. Termux has a “boot” plugin that should start Radicale every time the phone is turned on, but whether it will run reliably is another question.

Syncthing runs a discovery server that helps nodes/devices find each other when you are away from your home network, so it should still sync in most cases. on some routers, if it cant get around the NAT then files will be synced using Syncthing’s relay server, but you have the option to turn both of those off if you want either