
o365 Personal/Family and Business are compltely seperate & unconnected
On the home PC did you uninstall the pre-installed o365 Family trial via win add/remove dialogue and then start Word?
O365/Office when installed under a Win user admin account, and run from that admin account, auto logs in when the PC is started. There is no separate login for any component.
Win search for Word > Resulting shortcut > Rt click > Pin to task bar > start Word from that shortcut (hover mouse over the shortcut gives access to the 10 most recent docs)
Same for other core components.
Start eg Word open an old doc via recents/search
Rarely any need to access OneDrive itself.