I want to suggest a new step

Which tool is this about? Where is its repository?

Waydroid is a container-based tool to boot a full Android system on a regular GNU/Linux system (i.e. an Android simulator). It uses Linux namespaces (user, pid, uts, net, mount, ipc) and provides Android applications on any GNU/Linux-based platform.

The Android runtime environment ships with a minimal customized Android system image based on LineageOS, which receives frequent (weekly) upgrades.

Repository.

Which operating systems are supported by this tool?

Any x86_64 GNU/Linux with Wayland session and kernel module binder_linux.

What should Topgrade do to figure out if the tool needs to be invoked?

waydroid executable exists and $ waydroid status exits successfully.

Which exact commands should Topgrade run?

# waydroid upgrade, which stops running containers, downloads new images (if any) and extracts them.

Since it will kill any running containers without confirmation, one can use $ waydroid status to determine whether the container is running first, and allow user to save their work.

Running:

$ waydroid status
Session:        RUNNING
Container:      RUNNING
Vendor type:    MAINLINE
IP address:     192.168.240.112
Session user:   w568w(1000)
Wayland display:        wayland-0

Stopped:

$ waydroid status 
Session:        STOPPED
Vendor type:    MAINLINE