Hi there! Thanks for bringing your question here.
libASAF.dylib isn’t documented by Apple in any public developer materials, and there’s no official description of its purpose. However, based on the name, its code signature, and the frameworks it links against, it most likely relates to Apple’s spatial audio processing. The “ASAF” name strongly suggests Apple Spatial Audio Format or a similarly internal audio framework.
Even though it’s Apple-signed, it’s unusual for an Apple-provided library to appear in /usr/local/lib, since that path is normally reserved for user-installed tools (Homebrew, MacPorts, custom builds, etc.). Apple typically stores system components in /usr/lib or /System/Library/ and protects those locations with System Integrity Protection.
So, the most likely explanation is that some third-party installer, tool, or audio-related software placed this library in /usr/local/lib, even if the binary itself was built or signed by Apple. Homebrew flags it because its prefix should contain only files it manages.
If you’re concerned, you can move it out of /usr/local/lib, run brew doctor again, and see whether anything breaks. In most cases, removing or relocating it does not cause issues, because it’s not part of macOS’s protected system libraries.
If someone needs help identifying which software may have installed it, feel free to ask — please just write follow-up questions in German.