Thanks for that explanation. From your description, it seems you are using the Time Capsule as your wireless router, and that function seems to be working ok.
The first, easiest and simplest step is to merely restart the Time Capsule. You can either select it in the Airport Utility app using its Base Station menu > Restart... or unplug it for an arbitrary moment and plug it in again.
While you do that you might as well restart the modem also. Unplug it, wait a moment, plug it back in again.
Sometimes restarting the Mac helps if restarting the other devices doesn't.
Let the modem and the Time Capsule restart, which will take a minute or two. Wait for the Time Capsule's status LED to illuminate steady green. Then, reconnect to its wireless network (if necessary, by selecting it in your Mac's Wi-Fi menu), make sure you are connected to the Internet (simply load a web page) and start a manual backup.
See if that simple first step works.
If Time Machine remains unable to find the backup disk, the next step will be to have Time Machine "reconnect" to the backup disk using the procedure in this Discussion: Time Machine "the backup disk could not be found" - Apple Community. That link will take you directly to the procedure.
Please write back if Time Machine still can't find the backup disk after following those steps.