It seems the DOS version is not yet able to communicate with the hard disk.
FDISK is a completely different thing. It uses different methods (the BIOS) to access the drive data sectors to read/write, but by that way, it is not possible to access the hard disk REAL physical identification details (model ID, firmware version, serial number etc.) and self-monitoring data like temperature, health and so.
Generally this does not really depend on the hard disk itself, but more depends on the disk controller (chipset) which manages the hard disk.
Please try to make a photo (even by your mobile phone) and send to email@example.com about what the DOS version displays.
Even if it can't access the hard disk itself, it should detect the disk controller and this information may help to investigate the actual situation with that (or similar) chipset and add support to the DOS version.
The best would be if you can also use Report menu -> Send test report to developer option in the Windows version too. This way it is possible to check how the conttroller works and what kind of information it can provide.
Also you may try to configure a different mode for the disk controller. Disk controllers may work in IDE (legacy / compatible) or AHCI (native) or even RAID modes. In most cases, in the BIOS SETUP (which can be accessed usually by pressing the DEL or F2 keys before booting) it is possible to configure the operation mode of the disk controller / SATA controller.
Some chipsets provide no access to disk status in RAID mode at all and may only limited (or no) information in AHCI mode.
So at least for the duration of the test, you may try to configure the disk controller as IDE/Legacy/Compatible (the actual name depends on the manufacturer, the BIOS and so) and re-run Hard Disk Sentinel for DOS. Then it is possible that the status will be immediately displayed.
Just make sure to restore the setting to the original - otherwise the installed operating system may not able to boot.