I want to suggest a new step

Which tool is this about? Where is its repository?

PlatformIO is a tool to configure and compile embedded software – especially custom firmware for 3D printer.
The command "pio upgrade" is used to check if a new version (of the "Core") is available and will upgrade it, if needed.
(The other parts not in the core are the VS Code extension, which is therefore already supported, and the libraries used in each project)

This is their website, which has links to their git repository and documentation: https://platformio.org/

Which operating systems are supported by this tool?

Linux, Windows (and most likely on Apple as well)

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

On Linux the default installation path for the updater is: "~/.platformio/penv/bin/pio"
If it exists, invoke it.

On Windows it is according to documentation in "C:\Users\UserName\.platformio\penv\Scripts\", which should result in the path being "~/.platformio/penv/Scripts/pio.exe". (tested in Powershell on Windows 10)

Which exact commands should Topgrade run?

On Linux: ~/.platformio/penv/bin/pio upgrade
On Windows: ~/.platformio/penv/Scripts/pio.exe upgrade