Compare two String in Java with possible null/empty values, when one is null and another is empty it will return true

You can use a wrapper class overriding equals(Object) and hashCode().

public final class StringWrapper {

  private final String value;

  private StringWrapper(String value) {
    this.value = value;
  }

  public static StringWrapper ofValue(String value) {
    return new StringWrapper(value);
  }

  public static StringWrapper ofNull() {
    return ofValue(null);
  }

  public static StringWrapper ofEmpty() {
    return ofValue("");
  }

  @Override
  public int hashCode() {
    if (value == null || value.isEmpty()) {
      return 0;
    }
    return value.hashCode();
  }

  @Override
  public boolean equals(Object obj) {
    if (this == obj) {
      return true;
    }
    if (!(obj instanceof StringWrapper wrapper)) {
      return false;
    }
    String value1 = Objects.requireNonNullElse(value, "");
    String value2 = Objects.requireNonNullElse(wrapper.value, "");
    return Objects.equals(value1, value2);
  }

  @Override
  public String toString() {
    return "Wrapper - " + value;
  }
}

And tests covering the scenarios:

public class StringWrapperTests {

  @Test
  public void sameStringValues_ShouldReturnTrue() {
    StringWrapper first = StringWrapper.ofValue("a");
    StringWrapper second = StringWrapper.ofValue("a");
    assertEquals(first, second);
    assertEquals(second, first);
  }

  @Test
  public void differentValues_ShouldReturnFalse() {
    StringWrapper first = StringWrapper.ofValue("a");
    StringWrapper second = StringWrapper.ofValue("b");
    assertNotEquals(first, second);
    assertNotEquals(second, first);
  }

  @Test
  public void bothEmpty_ShouldReturnFalse() {
    StringWrapper first = StringWrapper.ofEmpty();
    StringWrapper second = StringWrapper.ofEmpty();
    assertEquals(first, second);
    assertEquals(second, first);
  }

  @Test
  public void firstNullSecondEmpty_ShouldReturnTrue() {
    StringWrapper first = StringWrapper.ofNull();
    StringWrapper second = StringWrapper.ofEmpty();
    assertEquals(first, second);
  }

  @Test
  public void firstEmptySecondNull_ShouldReturnTrue() {
    StringWrapper first = StringWrapper.ofEmpty();
    StringWrapper second = StringWrapper.ofNull();
    assertEquals(first, second);
  }

  @Test
  public void bothNull_ShouldReturnTrue() {
    StringWrapper first = StringWrapper.ofNull();
    StringWrapper second = StringWrapper.ofNull();
    assertEquals(first, second);
    assertEquals(second, first);
  }

  @Test
  public void firstNullSecondValue_ShouldReturnFalse() {
    StringWrapper first = StringWrapper.ofNull();
    StringWrapper second = StringWrapper.ofValue("qwerty");
    assertNotEquals(first, second);
  }

  @Test
  public void firstValueSecondNull_ShouldReturnFalse() {
    StringWrapper first = StringWrapper.ofValue("asd");
    StringWrapper second = StringWrapper.ofNull();
    assertNotEquals(first, second);
  }
}