I don't think this is so much a question of sources & corroboration as it is of language.
Regardless of the origins of the term "sideload", the language implies a non-standard practice. The prefix "side-" may be used in some software contexts to describe normal, non-deviant software, but only in cases where the software in question is considered auxiliary. In general, anything described as "side-*" is connoted to be surplus / additional / non-primary at best - adding that to the term "load" & the loading action itself is surplus/additional/non-primary. It's automatically considered non-standard.
> those devices don't have first party stores
This only supports the argument. If somebody felt an alternative term was required on Android because the first-party store was the primary source of software, the only reason they could have for needing such an alternative term would be to explicitly differentiate that alternative source as unofficial/non-standard.