This is not primarily a problem of the cooperation trains, I have the same situation with trains within Germany. DB-Navigator only tells you if a train is bookable right at the end, right before payment. Before that, it might show "there is high demand", but this is rather useless, especially when you have a school kid and want to book a train a the beginning or end of school holidays, when every train is in high demand. Your only chance with DB-Navigator is to play the whack-a-mole game where you run all the steps repeatedly until the very last step until you find a train you actually can book.

In the SNCF app I have this information right away, that is what makes the difference for me.