@DmitriPavlov: It is quite alright to use your own interpretation of the terms and suggest the projects you think are in the spirit of the question. I've tried to refine my criteria through my comments on why I think nLab, Polymath, and the two textbooks mentioned above don't satisfy one or the other of them. My model ultimately is Bourbaki as adapted to the internet and new ways and possibilities for collaboration it offers.

@DmitriPavlov: That is interesting and good to know! I was not aware of it. Their "About" sections suggest that they aim to be collaborative, but the reality may well be different.

@Fosco: $n$Lab in my view is not a systematic foundational text development enterprise. It seems to be more of an encyclopedia for certain areas of mathematics, although certainly online, evolving, collaborative and aimed at research mathematicians.

@Fosco: Thanks for the suggestions, but I am only looking for online projects that qualify on all the counts mentioned in the first line of my post, so online textbooks you mention don't come under its purview. There is no dearth of online texts which, of course, are also admirable, valuable and suited to our times.

@LSpice: Yes, thanks! How do I flag it? Polymath as I understand it is not for writing foundational research-level texts collaboratively, but for doing research collaboratively.