I found an answer here.
Elementary OS has the Gnome Control Center installed, but it's kind of hidden. You can try to open it from the command line with
gnome-control-center but it's blank. I first tried installing Gnome Online Accounts with this:
sudo apt install gnome-online-accounts
That didn't resolve the situation. Then I found the solution I've linked to:
Essentially the gnome control center only works when the desktop environment is Gnome. The command provided above sets the current environment to Gnome then opens the gnome-control-center inside of that environment. Allowing it to load properly.
So it'll work if you run this:
env XDG_CURRENT_DESKTOP=GNOME gnome-control-center