Once I logged into the Synology NAS using Firefox and began the setup again, I authenticated to the Synology C2 website, was taken back to the NAS, and was able to complete the setup. That's a little frustrating in today's day and age, and something to be aware of.
A web browser pops up to connect to the service, but the Synology C2 service does not support Microsoft Edge, so in order to complete the initial setup, I had to first login to my Synology device with Firefox, and then begin the process again. There was a minor issue when setting up the C2 backup target. Synology's C2 service is listed under "Synology" instead of "Cloud Service," which is a little odd if anything I'd expect to see it in both sections, but it's a minor quible. Everything from backing up to a local folder, another NAS device, rsync, or cloud services from companies like Amazon and Microsoft are available. After installing the package, you're greeted with a Backup Wizard, along with a list of all backup endpoints you can select.