When I play, which is not all that often, I design a character who has strong motivations and will drive things in directions that I think are interesting.
This is same for me, as in I do not often get a chance to play sadly.
With the current player who is running a game for us, they have a setting with an unfolding event (brought upon by our characters - a plague).
When I selected my bard character, I looked at the various nations (I think it is the 7th Seas setting) and formulated a backstory as well as the languages he would know. If the campaign continues long enough, my character may develop personal goals but as of right now, my goals are pretty much party goals and that is likely because of the in-game fiction.
When I GM, I look to what the players seem to want to do with their PCs, and establish situations that will provide opportunities to do that. What exactly that looks like, and how intense it will be, depends on the system. For instance, Burning Wheel or In A Wicked Age is more intense in this respect than Classic Traveller or Torchbearer 2e.
When GMing 4e D&D, which in its default presentation is heavily setting-oriented, I looked to the players to foreground those parts of the setting that they wanted to engage with (via their PCs). That's why our campaign made certain elements - the Raven Queen; the Lattice of Heaven; the sundering of the Elves, and their reunion; the nature and fate of the Abyss; and some other stuff too - central. While other parts of the default setting were of much less significance in our game.
My role wasn't just to bring those elements that the players had foregrounded into play; but to also present them in ways that would require the players to make hard choices - eg Will restoring the Lattice of Heaven have other consequences that sit at odds with the aspirations the players (as their PCs) have? Is it possible to permanently defeat the Abyss without restoring the Lattice of Heaven? Etc.
So this is not about presenting the setting in a "neutral" fashion. It's about pushing hard where that will be interesting for me and for the players.
Given the underdevelopment within D&D's character personality/drive/alignment system we expanded significantly on the TIBF system, attempting in a similar vein in what you're doing with more polished systems.
To give you an example.
In our last session the artificer who's personal goal is very much one of exploration and knowledge of science/tech
(think Numenara) and it's role in the universe, had a meeting with Elminster who has a ward whose origins are along those lines. In any event the social encounter saw him gain a map of a rift which has occurred south of Candlekeep which promises Numenara artifacts/knowledge with the idea that he will investigate same with the ward and report back to Elminster on his findings.
This was all done through an easy enough Skill Challenge, but the real reward was that as the ward was escorting him out, she mentioned to him that Elminster has a book on Numenara but that she is unable to remove it from the premises - HOWEVER - she knows that Elminster is set to make an appearance the next day, at the Final Council Meeting before the push against Tiamat and Cult of the Dragon. She has no idea why Elminster has kept the tome a secret from the PC but she is willing (as she took a liking to the PC - real purpose of the Skill Challenge success) to have him access it while Elminster is away at the Council Meeting.
The hard choice I presented him being that his party needs him at the Council Meeting to help sway the Council Members.
He has a TIBF which states:
Unlocking an ancient mystery is worth the price of a civilisation
Now, he earns an Inspiration point and an Experience Point if he adheres to his TIBF, thus disappointing his party members at the Council Meeting with his absence.
To put it into perspective Experience Points are extremely valuable and are one of three ways to increase in level in our campaign, we do not use the standard tables.
The Council will deliberate for 3 days, but missing the 1st day may certainly make things difficult for the rest of the party.
So, I lean into the TIBF system a lot (and encourage them too), presenting hard choices, but the players ultimately choose what their characters do.
Sadly for now, much of the legwork on this is done by me, but they do like these hard choices. The snag being that it requires me to very much be aware of their characters' TIBFs in order to find ways to apply them. For sure it is extra legwork on my side.
