No, Songtrust can not scan audio to detect the use of your beats.
When you are asked to link a recording to your songs, we are looking for what is called an ISRC. The ISRC is a code that is usually assigned by distributors and are unique to each of your recordings. This is then used to track your song data across many platforms like Spotify, YouTube, etc.
If you released your beat as a song through a distributor, it would be assigned an ISRC. However, if I made a new song that contains your beat, that recording would have an entirely separate ISRC.
As a producer, you would need to add each new song that is made with your beat with the title, new writers, splits, and the new ISRC. This information is necessary in order for us to collect your publishing.
It is important that you come to an agreement with anyone who is going to be using your beats so that you will be able to establish who is entitled to publishing and how the song should be registered.
If people are using your beats without your permission, it would be best for you to consult a legal professional.
You can learn more about producers and songwriting credits here.
You can also learn more about how to decide on splits here.