The OpenPuck project allows the Steam Controller to emulate console controls, among other uses

A work in progress, but a very intriguing one.
XDA Developers on MSN

This open-source puck lets you use your Steam Controller on Xbox, Switch, and PlayStation consoles

It's cheap to build, too.
Hackaday

DIY Steam Controller Puck Offers Xbox, Switch, PlayStation Emulation Modes

Valve recently released a new version of the Steam Controller, which features a wired USB puck that serves both as charger ...
PC Magazine

Steam Makes It Easy to Find Games That Support PlayStation Controllers

While you can use Sony PlayStation DualShock and DualSense controllers with Steam, it's been hard to find games that support them. That's changing thanks to a new Controller-Friendly Hub. Most Steam ...
TechSpot

Steam adds official support for DualSense and DualShock PlayStation controllers

Game time: Valve has long made it easy for gamers with an Xbox controller to find something compatible to play on its Steam platform. The experience has not been as seamless for PlayStation DualShock ...