It comes from literature I did read over a decade ago, which titles I no longer have, which argued (in a very summarised sense), that science as we know it today is only possible due to the development of social institutions and methodology that have been refined over centuries (and arguably, are currently in an evolving process), in ways that make it fundamentally different (in its workings, its results, how it is envisioned and how well it procures reliable knowledge) from what the natural philosophers of antiquity did, ultimately requiring an ample social system for it to even be viable. You will notice that the majority of attempts to schematize the scientific method include either reporting or publishing, or delegate the task of replicating experiments to third parties.

The page for Science appears to also contradict the “hard definition” when it describes science as spanning most of human history, long before the modern institutions of formal publication and peer review, and doesn’t describe them as mandatory at all. Definitely doable at home, as far as I can tell.

Sure, you can see sketches of what we currently consider science in the historical development of astronomy across Mesopotamia, Egypt and elsewhere (lacking the modern core methodology), or in Newton's writings about alchemy (lacking communication), but most of it was intertwined with mysticism and esotericism. You can use a more lax definition if you want, but I think that in doing so, you're making the concept lose meaning.

That’s not to say that scientific collaboration isn’t valuable, btw… I just can’t find any basis to support the idea that if it’s not published in a formal academic journal, then it’s definitely not science, and that science CAN’T happen without the involvement of the institutions.

150 years ago, the contemporary institutions of formal publication and peer review didn't exist, but equivalent processes were already starting to take form. These contemporary institutions aren't as important as it is that the tasks they fulfill do get done in one way or another.