A device with 2 hard drives?

I want to buy a notebook with a hybrid hard drive, i.e. Consisting of 1TB SATA and 128 GB SSD. I wanted to ask what problems might arise and on which of the hard drives my files are automatically saved.

It's not a HYbrid hard drive.
There are just 2 hard drives and the data is always stored on the main data carrier (mostly C. Saved where your Windows is on it.
The only problem is that you only have to save larger files on the HDD in the installation process or simply move them over the hard drive D

So do I have an HDD and an SSD hard drive in my notebook?

Yes

And why do I have to save larger files on the HHD?

Well if you have 128 Gb on the SSD, the Ratz is full
And with the HDD you have 1000Gb because it fits more
To keep in mind that Windows is already installed on the SSD and the yes also takes up space

Programs and data are usually installed on the primary disk, unless otherwise specified. If there's no other partition, this is usually C: \\ Windows.

If, as in your case, another hard drive is installed and it is also not partitioned differently, it is declared with the drive letter D: \\.

Unless you set it differently, your data will be installed on C: \\ Windows.

I have partitioned my hard disks and each partition has a name I named, e.g. D: \\ Programs, E: \\ Private etc. And change the respective paths. I personally find it more structured.