I just did this back in August.
I had an old computer which got fried but the HDD was okay. As with you, the OS was on it but it was Windows 7 and I was moving to Win 10. I bought a new machine with Win 10 and kept the two HDDs from my old one. Like you, I have USB converters for the disk drives so I can read them.
Once I had the new machine set up the way I wanted it I put my old system drive in one of the USB converters and copied any files I wanted to the appropriate location. Then I put the old drive in a cabinet in case I decide I need something else later.
I had an old computer which got fried but the HDD was okay. As with you, the OS was on it but it was Windows 7 and I was moving to Win 10. I bought a new machine with Win 10 and kept the two HDDs from my old one. Like you, I have USB converters for the disk drives so I can read them.
Once I had the new machine set up the way I wanted it I put my old system drive in one of the USB converters and copied any files I wanted to the appropriate location. Then I put the old drive in a cabinet in case I decide I need something else later.