office for 2 machines

I bought Office for home and student 2019 and am using it in my pc. I also have a 2010 MS word that will become unsupported in 2010 put aside.

Office 2010 is a Windows version only. Since you've noted Office 2019 is on your PC, then it is course also a Windows version.

Neither of these can be installed on your Mac. Not as a native Mac application. You'd have to install a VM, such as Parallels or VMware, install Windows in the VM and then your Windows version of Office within that.

If Office is your preference, what you should have done (particularly for two or more computers) is purchased Office 365. You can legally install Office 365 on up to 6 computers, Mac or Windows. And even using just two Office 365 licenses is cheaper than upgrading the more expensive perpetual license versions every 3 years or so.

Use Office on whichever computer you want to. We don't know which setup is best for you. Personally I would get an Office license good for both computers.