BSD or MIT license would be nice.

AGPL would be better

Amazon and other cloud providers avoid AGPL, so I think it's closer to the intentions of the OP.

I think the license choice is great. It allows noncommercial use, modification, and redistribution. It’s not “open source” according to the champions of the term (since it violates the use-for-any-purpose requirement) but I’m a huge fan of this license and license several of my projects CC-NC-BY where AGPL would be too heavy-handed.

I think your choice is very appropriate.

And it is open source.

Probably not OSI-open source or FSF-open source but it is open source, period.

"It's not recognized as Open Source by the Open Source body, and doesn't meet the criteria of Free/Open Source Software, but is Open Source" is a bit like saying "I used GMO and petroleum based pesticides, but my produce is all organic."

But here the source is open!

Why should we restrict the meaning of Opel Source, a societal mouvement since decades, to a list of criteria that FSF or OSI decided?

Open source is not a trade mark by FSF or OSI.

OP did not say it is free/libre software, but just open source, which it is.

We don't need "source available", just open source is correct.

PS: can you define the open source body in your previous comment?

Why should words like "organic" in relation to food mean without pesticides? I mean all carbon and water based life forms are organic, right?

I can define Open Source easily, using the OSI definition.

There is not a trademark for Open Source because they failed to secure the trademark, but we have decades of use for the term meaning something specific.