The official terms at play here are "modular" and "mobile" home. These are the terms that define the kind of house you're thinking of. "Mobile" homes are constructed to a separate set of parameters, and are not "permanently" mounted on the property. (Regardless of how "permanent" you make the attachment for a "mobile" home, it is still titled separately from the land.)

Modular is the term of art for a factory-built home that is installed on the land and becomes titled as "real property" with the land its self, search for "modular home builders." Nearly every modular builder also builds mobile homes, so when you go to their site, look for "available as modular" or "modular" as a category or search term.

FWIW, "modular" and "mobile" are actually built to two different manufacturing requirements and specification, and why "mobile" homes are often disallowed in towns and cities, amongst other reasons, is that HUD controls the specs for "mobile" while "modular" must meet local building codes.

It seems one way is to post a link to HN of a provocatively expensive glossy model and wait for the links in the comments to roll in.

Start from searching "manufactured homes" and pay attention to the companies that "deliver" them without axles. Double-wides will be better looking in general.

Once you find one, you can use that company to find if they're part of a "factory build housing alliance" or similar (eg https://www.factorybuiltwisconsin.com/about-us/ ) and spread out from there.