I think this is an important point, the distinction between the “particular”, within the judgement, and the “real existent”. Notice that he is not calling the independent ‘thing’ “the particular”, but he puts the particular inside the mind, in the idealist way which makes the object an idea in the mind. So he maintains the Kantian unknowability of the independent, so much so that it cannot even be said to consist of particulars or objects, as these individuals are within the thinking, and the independent is merely “the existent”.
So I think, that what is the case here, is that “nothing particular is true” means that there is no real independent particulars. All we have is “the existent”. I think this may be important toward understanding the reality of contradiction. The non-contradiction law applies to what we say about things in predication. Contradictory predicates cannot be true of the same object at the same time. Now Adorno is removing “the object”, or “particular” from the independent, to make it a mental construct produced for the purpose of applying that law. Now we have only “the existent” as the independent, so we have no basis for the application of that law.