Settings and Lores
Okay okay... depending on who you ask they may say there is a setting and lore for OS-tans, and I say no for OS-tans having a setting and lore.
If it is said that "The variations vary from person to person, and it can be said that there are as many different OStan worlds as there are painters." on the Heika Love page, then this should really mean that each person's lore and setting for OS-tans is different, therefore no real "canon" anyway.
The worldview and settings of OS-tans at Futaba☆Channel basically have no clear author. This is because the idea of OS personification was conceived not only in the form of illustrations, but also in the form of short stories that were published at the same time. The illustrations and short stories influenced each other, and several character traits were accumulated to form the general character of OS-tans. Therefore, except for the original design and initial setting, no clear author or individual decided on the setting. It can be said that OS anthropomorphism itself was only a temporary fad or a spur-of-the-moment proposal. Therefore, no specific individual or group controlled the setting or handling of these settings.
Even on one of the image vaults for OS-tans has a FAQ stating that "There is no official setting. The designs and personalities vary depending on the person who draws them." though it is affiliated with 2channel (neither was the OG image vault anyway) so I think it shouldn't matter.
There was a site which was said to be a site that supports and explains "OS Musume" from Futaba ☆ Channel / 2D Ura@Futaba but it appears to have not been updated very much.