The other backend/provider "plugins" including todo.txt are disabled by default:
https://gitlab.gnome.org/GNOME/gnome-todo/-/blob/master/meson_options.txt#L7
and that means you'd have to compile it yourself (quite a few dependencies, and figuring these out, for me it failed with an error).
I don't know if building the "plugins" would enable a menu where one could select them. It could be done in dconf-editor (GUI) or gsettings:
$ gsettings get org.gnome.todo default-provider
'local'
$ gsettings range org.gnome.todo default-provider
type s
$ gsettings describe org.gnome.todo default-provider
The identifier of the default provider to add new lists to
This applies to Ubuntu 22.04 and
$ apt show gnome-todo
Package: gnome-todo
Version: 3.28.1-6ubuntu1
Priority: optional
Section: gnome
Origin: Ubuntu
Maintainer: Ubuntu Developers <ubuntu-devel-discuss@lists.ubuntu.com>
Original-Maintainer: Debian GNOME Maintainers <pkg-gnome-maintainers@lists.alioth.debian.org>
Bugs: https://bugs.launchpad.net/ubuntu/+filebug
Installed-Size: 485 kB
Depends: libc6 (>= 2.34), libcairo2 (>= 1.2.4), libecal-2.0-1 (>= 3.33.4), libedataserver-1.2-26 (>= 3.33.4), libedataserverui-1.2-3 (>= 3.33.4), libgirepository-1.0-1 (>= 0.9.2), libglib2.0-0 (>= 2.51.2), libgoa-1.0-0b (>= 3.5.1), libgtk-3-0 (>= 3.21.5), libical3 (>= 3.0.0), libjson-glib-1.0-0 (>= 1.5.2), libpango-1.0-0 (>= 1.14.0), libpangocairo-1.0-0 (>= 1.14.0), libpeas-1.0-0 (>= 1.17), librest-0.7-0 (>= 0.7), gnome-todo-common (>= 3.28.1-6ubuntu1), libgnome-todo (= 3.28.1-6ubuntu1), evolution-data-server (>= 3.17.1), gsettings-desktop-schemas
Breaks: gnome-todo-common (<< 3.28)
Replaces: gnome-todo-common (<< 3.28)
Homepage: https://wiki.gnome.org/Apps/Todo
Task: ubuntu-desktop, ubuntu-desktop-raspi
Download-Size: 165 kB
APT-Manual-Installed: no
APT-Sources: http://de.archive.ubuntu.com/ubuntu jammy/main amd64 Packages
Description: minimalistic personal task manager designed to fit GNOME desktop
GNOME To Do is a simplistic personal task manager designed to perfectly fit
the GNOME desktop. Designed from ground up to seamlessly integrate with
the GNOME desktop environment, To Do enables you to be as productive as
you want.
Related: gnome-todo (Ubuntu "To Do") lacks help, how does it store lists?