Hey there, @saturn144!
I'm afraid that @Kelvin is right. You won't be able to boot from a different Windows 10 installation that is tied to another computer. (The operating system is tied to the motherboard of your computer, whereas the HDD is just a carrier for the system files). However, you shouldn't face any issues if you use it a secondary storage for your Steam gaming. Moving the Steam installation & games is rather easy and they have a pretty detailed tutorial in their official knowledge base on how to do it, so I'd advise you to go check it out.
I'd also highly recommend performing full backups of your files somewhere off-site before tampering with the storage configuration in both PCs!
Good luck! Keep us posted if you have further questions.
SuperSoph_WD