Update the firmware of the hard disk.

[AMKarogin]

Good day.
There is a monoblock HP ENVY 23 (23-d270er) running Windows 10 x64 Home for one language.
Having decided to check the firmware updates for my components, I went to the support section of this product, but did not find my operation system. There were only Windows 8 / 8.1. Choosing 8.1, I saw that there are firmware updates for the BIOS and hard drive, realizing that the firmware flashers are not so dependent on the operating system, I was not afraid to download them from 8.1. The BIOS was updated without problems, but there were difficulties with updating the hard drive firmware. The hard drive in this monoblock model is from Seagate with a capacity of 2 TB and a speed of 7200. In the support section there is also an update for Hitachi hard drives. Having chosen the program of the flash driver I needed, I tried to flash the hard drive. The installation was over, the computer rebooted, but the disk was not flashed. Having tried the second time, when I started the program, I paid attention to the inscription supported devices, where I did not find my hard disk, there were only 2 disks: for 500 GB and 1 TB. Why is HP misleading? How can I go to the support page of my monoblock of my configuration, and not the general line?
I found a document describing my monoblock https://support.hp.com/ru-ru/document/c03859233 in which I did not see hard drives from other manufacturers, and indeed only my hard disk in the document, as if there were no other configurations. This confused me even more, why in the support section there are firmware from devices that were not in the configurations of this line. Help to understand, thanks in advance.