Suggested fix: use a random UUID string as boundary. It will be next to impossible get bump into such value.

public MultipartContent() {
   super(new HttpMediaType("multipart/related").setParameter("boundary", "__END_OF_PART__"));
}

=>

public MultipartContent() {
    this("____" + java.util.UUID.randomUUID().toString() + "___");
 }
 
public MultipartContent(String boundary) {
    super(new HttpMediaType("multipart/related").setParameter("boundary", boundary));
}

Wouldn't it be more efficient to fix and use a constant (static final String, some random UUID) instead of creating a new UUID everytime the instance is created? (I'm genuinely asking.)

I think, generating UUID each time when an instance of MultipartContent is created is a very little overhead.
Having any static string value publicly available will significantly increase the likelihood of being included into someone content. (At least it's possible). With a random value it's very unlikely to repeat that value.