Because you say "It happens only with the picture taken with the app" I assume that you have enabled sync in the Lightroom Classic catalog and that other images added to Lightroom mobile do sync? In that case, the most likely explanation is that the camera pictures do sync as well, but you just can't find them. Look for a 'From Lighroom Mobile' collection set, or go to 'All Photographs' and check there.
I have the same problem: If I take a photo by the LR camera (Samsung Android 10) in form DNG it will not be synchronized bei LR C. This pictures doesn't appear in LRC anywhere. (in the folder IN LR mobile I can see it).
Is this photo in form JPG the synchronization beetween LR mobile and LR C is o.k and I can see them in the desktop version.
In the web version of LR is also all o.k. Here I can see the DNG pictures (I think, because of the directly connection with the cloud).
I have not found any attitudes in LRC with which I can support the synchronisation of DNG pictures from LR mobile.
(sorry, my english is not so good: I hope, you understand me....)