In an official statement, the Steam client for the Mac will lose complete support for macOS Big Sur very soon.
Steam will Stop Working on macOS Big Sur After October 15th Due to Lack of Support from Chrome
Steam will no longer work on macOS Big Sur from October 15th of this year. The reason for that is the reliance on Chrome which has also lost support for Big Sur.
If you want to keep on using Steam and access your library of games, you have to update your Mac to at least macOS Monterey. But, if your Mac doesn’t support that at all, then you might want to get a more recent Mac.
The October 15th deadline won’t likely be extended at all, and it’s best you sort things out way before that, and the best course of action, is a software update.
