You’re spot on-there’s never been an official Service Pack 2 or 3 for Windows 7, and anything labeled as “SP3” is an unofficial bundling, usually by third parties. I’d avoid those entirely; they’re often out of date or can contain dubious modifications.
If you absolutely have to keep Windows 7 running (say, for legacy app support), stick to official Microsoft sources. After installing SP1, use the official “Convenience Rollup” from 2016 to cover most updates (KB3125574), then grab the last available security rollups directly from the Microsoft Update Catalog. For extended support, ESU licenses are required, but be warned, those ended for most users in January 2023. Anything beyond that is risky and not supported for the general public.
Best bet is to isolate those machines from the internet if possible, and always use trustworthy sources. Any site claiming official “SP2” or “SP3” for Windows 7 is doing it unofficially-so use caution!