If you are using the fan-made HD Project or other mods for the original RE4, mod installers sometimes replace the steam-api.dll with an older version.
Check antivirus/quarantine
Launching Resident Evil 4 only to be blocked by a "steam-api.dll is missing" or "steam-api.dll not found" error is a frustrating experience. This specific Dynamic Link Library (DLL) file is a critical component that allows Resident Evil 4 to communicate with the Steam client. It handles essential background features like achievements, cloud saves, multiplayer connectivity, and digital rights management (DRM) verification. steam-api.dll missing resident evil 4
Sometimes the error is a symptom of a larger system issue. If you are using the fan-made HD Project