Most likely the Windows 7 key that you used was Retail, since it worked for
you on a new computer. Therefore, your Windows 10 Home license should be
transferable to a new computer in the future.
Before upgrading Home to Pro, in order to make the transfer possible,
you should deactivate the Home serial on the computer before doing the
upgrade install of the Pro version. It is important that an Internet
connection be available when doing that, so a connection is possible
to the Microsoft servers.
Deactivating the computer is done by running the Command Prompt (cmd)
as Administrator and entering one of the following commands
(whichever one works for you) :
slmgr.vbs /upk
slmgr.vbs -upk
This is required, since Windows only allows any one license to be installed
on only one computer at a time.
Note that the reuse of the Home serial is not guaranteed, since there
might be other factors in the future, which include Microsoft changing
its transfer policies.