Hi Coylie3.
I'm David, and I'm happy to help you.
The HDD that has Windows 10 installed should work properly connected to Windows 11 without having to reformat it.
However, adjust the BOOT priority in the BIOS of the Windows 11 computer leaving the SSD at the top priority. This way, you prevent the computer from starting Windows 10 from the HDD instead of Windows 11 from the SSD.
I hope this helps. Feel free to ask back any questions.