Aaaand the thread has turned into another Player vs GM Agency debate.
That kind of was the original question: how the dm should adjudicate the class's fluff, when the mechanics technically only imply that you should.
Strongly imply, I'll agree, but Rules as Written you shouldn't do much of anything. So the question is about asserting more dm authority than RAW without being a doodiehead about it.
(Which is a subset of the cliché argument that we keep repeating. The trick is to focus on not being a doodiehead in the first place, which isn't that hard, and the rest is downright easy.)
My ultimate final answer to the first question: each
character is going to have a slightly different answer. Your best bet as a dm is to have a conversation with the warlock's player and figure out how to best combine the player's vision, your own vision of the world, and the roleplaying opportunities presented, in a way that won't overstay its welcome. But when I've played essentially the same warlock character in multiple campaigns, that answer was different each time.
For example, I play celestial warlocks as being essentially clerics (though more Orders Militant that priests per se). But what that means depends a lot on the details of the worldbuilding (what churches exist, what they care about, etc.) and so the final result was significantly different in terms of roleplay despite having the exact same build. Because they were different dms running different games in different settings.