What Eureka did was private label some machines for Walmart under the GE name. I was unaware there was a steam cleaner, but there were also a few uprights both bagged and bagless, as well as at least one canister vacuum.
Eureka was at one time its own independent company(Eureka-Williams Co.) and then was bought by WCI(White Consolidated Industries - a descendent of the White sewing machine company and the White Motor car company) which later in 1986 was bought by Swedish Electrolux. In the last few years Electrolux sold the Eureka Division to a company called Midea but still retained the Sanitaire division until last year when they sold it to Bissell.