Not enough memory on the PS4 even though a 1TB hard drive is connected?

Today the Ps4 wanted to pull an update. Because it always had too little storage space, I got a 1TB external hard drive and it can also be used as expandable storage. As I said, he wanted to do an update today and tells me again that there's not enough space. Will the hard drive now only be used for newly downloaded games and will the updates of the old games remain on the internal memory?

The older games each have their folders and subdirectories, and if these structures are created on the internal hard disk, then the corresponding update files are also copied into the folders and subdirectories of the older games on the internal hard disk.