Targeting the Player's Intrinsic and Extrinsic Motivation while designing quests will improve the player's experience.

What do we want as a developer? To design engaging and immersive experiences for the players. We are the directors of our own game. If we want them to experience any particular emotion, we create for it. Each quest we design is expected to end the experience with a specific feeling connected with the player character's character development. We should target the intrinsic Motivation of the player while designing the extrinsic motivation.
#1: Why is Intrinsic Motivation as important as Extrinsic?
Before I begin, let us recap Extrinsic and Intrinsic Motivation.
Extrinsic Motivation - the one we design explicitly to help the player progress, accomplish their goals, and helps them avoid punishment.
Intrinsic Motivation - the one where player set for themselves, which makes them happy and improve their self-esteem.
It's easy to target Intrinsic Motivation if their action results in feedback in the game world. However, it shouldn't be tracked explicitly or acknowledged anywhere else but in the game world.
Intrinsic Motivation targets the short-term goal of the player. But, unfortunately, it's an intrinsic motivation to impact a challenging long-term goal.
If players can't make up Intrinsic Motivation, we are doing something wrong. If there is only one playstyle in a design, it is hard to form intrinsic Motivation because extrinsic Motivation will provide the player with the Motivation to play.
A good balance between the two motivations will help players invest long-term. Therefore, explicit Motivation should be higher to help them progress, while a small amount of intrinsic Motivation will help their pursuit of extrinsic Motivation.
#2: Example: Hogwarts Legacy
Recently, I've been playing Hogwarts Legacy and thought about an idea during specific missions.

In Missions involving Poachers (there are plenty), the game provides you the Extrinsic Motivation - an objective to clear and what actions are needed for an extra reward.
In completing these missions, the player progresses the quest, and the extra reward gives them progress in challenges which in turn provides extra rewards. Both are explicit rewards that can be tracked in the status bar.
What sort of Intrinsic rewards can we help players create here in this quest space?
I had an idea of placing trapped beasts around the area.
