This essential plugin for the Steam Deck does a better job telling you how your games will play than Valve can manage itself

Saints Row IV on the Steam Deck showing a Gold ProtonDB compatibility badge.

As good as the Steam Deck is, by virtue of being based on Linux and not Windows, compatibility issues are always lingering. Sometimes it's down to anticheat, sometimes other factors, but it's less clear-cut than on an ROG Ally at times if you'll be able to play at all.

Valve does an insane amount of testing and lists Steam Deck compatibility in its listings. But it's not the most detailed, and there have been times in the past where even "Verified" games had significant problems.