When I'm a player as the game is happening, I want to say (author?) what my player is trying to do/thinking at that moment and explore the world/try things, and not author other things about the world (I don't enjoy it). I am happy to help author other things out of character between sessions.
Checking if my sister who is already established as a scholarly type knows someone at the library seems great. Stating that my nebulously defined sister knows someone at the library in a particular are doesn't to me.
You have it backwards. Declarations are not the player doing some kind of proactive authoring of specific stuff & cross referencing during play to check if you wrote about a specific thing earlier, it's simply declaring that you have a cousin or whatever who [fill in the blank right now after it became relevant]. At that point the character didn't suddenly gain a brother who worked in a library, they always had that brother who worked in the library & it just wasn't relevant till now. The noble's player didn't write that he has an uncle who runs a shipping business, the player declared it just now & the character always had it Same thing with the sister who is a high priestess of Selune & all the others, just now retroactively forms into existence. It works both ways but 5e PCs are "sunglasses people" in a lot of ways that limit the GM's ability to do that. When this kind of gameplay is in use the GM needs to control what's ok or not & have the ability to hold a PC's background/character fractal elements to the fire in return just as the GM needs to track monster HP during combat.
Not only does this allow you as a player to "say (author?) what my player is trying to do/thinking at that moment and explore the world/try things" it allows you as the player to form your character's backstory & place in the world as it becomes relevant while also driving the plot & direction of the campaign so a player is never faced with "ugh, I wrote this cool backstory that's totally the wrong fit for this campaign & is never going to come up". The possible downside of that to some players is that the story is formed collaboratively during play by everyone at the table & the GM needs to be able to maintain a tighter leash on it.