The SSD should be seen in the BIOS.
If you install Windows 7 on the SSD then it may create a boot menu with both Windows 7 and 10.
After you add the SSD boot the computer see what boots up. If it is Windows 10 on the HDD then you can modify the boot to add Windows 7 on the SSD. I added Windows 7 with a program called
EasyBCD. With EasyBCD I can make either Windows 7 or Windows 10 the default O/S.
I have a computer with 3 drives:
DRV1: Samsung 870 EVO (1TB 2.5" SATA SSD) Windows 10 Pro
DRV2: Samsung 870 EVO (1TB 2.5" SATA SSD) Data
DRV3: Samsung 870 EVO (1TB 2.5" SATA SSD) Windows 7 Home
When I boot the computer there is a boot menu:
I can select to boot into either Windows 7 or 10. However, if I do nothing then the default Windows 10 will boot after 30 seconds.