Oops, try taking a second look at your own links! I said "Sideloading as a term of art originally, in practice came into usage for transferring media to devices".
Your first link actually fits the description I gave, yet you're presenting it here as if unacknowledged.
Most of the usages you link to are in the paradigm of rom flashing or physical media data transfer, and don't even have the upshot of implying that "install" means download from preferred distributor, which is critical since that's what this whole thread is about. Hilariously, even your own links contain numerous casual references to "install" to describe the ordinary act of transferring files into the phone outside of the play store. Which is devastating for your point if your point is that sideloading is supposed to be exclusive term for that action, and that "install" has a long-standing and specific usage as meaning "distributed from Play Store."
Scattershot usage from people flashing ROMs or finding workaround hacks for hardware errors don't demonstrate that that vocabulary was as widely understood in the public consciousness as a settled meaning for sideload much less that the term install exclusively refers to downloading from the Play Store. And again importantly for this thread, it actually shows an evolution of the term that predominantly was about workaround hacks and rom flashing, which has now grown to comprehensively mean any installation of an app from outside the Play Store. If anything, that's a demonstration of a neologism.
And as a kid who grew up on Windows computers in the late '90s and early 2000s, it astonishes me that I have to say this but computing existed before 2009, and gives us a history from which we can draw when figuring out the established use of terms.
And again, as I already said, this sideload/install usage is unique to Android, not observed on Windows, Linux or even Apple. Giving me a bunch of links to a form of usage that I already accounted for in my own comment, and not addressing the more important part of my comment about the prevalence of install as a distribution neutral term, disregarding the history of computing prior to Android and outside of Android is an unfortunate misunderstanding of what your links do and don't say in this context.
2009 https://xdaforums.com/t/android-market-updates-on-sideloaded...
2012 https://xdaforums.com/t/app-wifi-band-switcher-switch-betwee...
2014 https://xdaforums.com/t/q-att-htc-one-m8-not-working-explana...
2020 https://xdaforums.com/t/app-mono_-flipfont-custom-ttf-instal...
This is a long standing term of art. If you're ignorant of a big part of the industry, that's on you.