Your rephrase here is spot-on. The link that I posted for that name (self.request) is a link to the most brief description in the docs as to what’s happening here.
I would change the wording slightly here in the interest of precision. You wrote:
I would consider it somewhat more accurate that the self.request object contains a reference to another object. That other object is an object of type User and is given the name user. That user object can contain references to yet more objects.
(Is this difference in wording important? Yes, under some circumstances. In many cases you can ignore the difference, but you should always be aware of it.)
Oops - typo. That should have been self.request.user. I had objects on the brain.
Yes, that would do it.
No worries, we’re here to help.