Intel Core Duos can run 64bit, but its still optional.
its up to you if you want to try it or not, but it will need you to download and install the 64bit version.
And you probably installed openSUSE 32bit, as its the default option on the download page, so openSUSE did not install 32bit, you did.
And the 64bit is not a true “upgrade” in a traditional sense.
Its an optional kernel that might or might not give you better performance.
Like I said its not like going from a Ford Pinto to a Ferrari