My goal is to get all moments of some user using public API. I've found this documentaion, but, as I understood, it is aimed to creating Mini Programs, which doesn't suit me. The most desirable way is just to send one request with user's credentials. Is it even possible, and if it is, how do I approach it?
If you are looking for what's possible on the web side of things (no MiniProgram), you need to refer tot the Official Account Documentation (https://developers.weixin.qq.com/doc/offiaccount/en/Getting_Started/Overview.html). As far as I am aware, only public information of users can be retrieved, and it does not include their Moments.