I found the local storage: /home/<user>/.local/share/evolution/tasks/<id>/tasks.ics and /home/<user>/.local/share/evolution/tasks/system/tasks.ics for "Personal"
Running $ gnome-todo -d prints
23:28:38.0742 GtdProviderSelector: DEBUG: Adding provider local
23:28:38.0761 GtdProviderEds: DEBUG: Task list 'Personal' successfully connected
23:28:38.0761 GtdProviderEds: DEBUG: Task list 'test' successfully connected
23:28:38.0818 GtdTaskListEds: DEBUG: ECalClientView for tasklist 'Personal' successfully acquired
23:28:38.0819 GtdTaskListEds: DEBUG: ECalClientView for tasklist 'test' successfully acquired
23:28:38.0833 GtdTaskListEds: DEBUG: Personal: GNOME To Do API version 1
23:28:38.0837 GtdTaskListEds: DEBUG: test: GNOME To Do API version 1
Searching for https://github.com/GNOME/gnome-todo/search?q=%22Adding+provider%22 leads to https://github.com/GNOME/gnome-todo/blob/master/src/gui/gtd-provider-selector.c#L273
If you dig around, there should be several more "providers", e.g. "todo.txt", so I assume this is a buggy package.
Edit
Also see https://askubuntu.com/a/1272813/1029310
/home/<user>/.config/evolution/sources/system-task-list.source contains the configuration of the "Personal" task list.
Edit
The other "providers" are disabled by default and would require building from source. See https://askubuntu.com/a/1415059/1029310