Exactly, finesse is the name of the game for sure. There is a wide spectrum between uninterested and not-desperate. Appearing that you are desperate to get out

Exactly, finesse is the name of the game for sure. There is a wide spectrum between uninterested and not-desperate. Appearing that you are desperate to get out of your current job is a far bigger red flag in most interview processes than appearing "not that interested". It's like the other side of the coin of people who are super paranoid of getting fired if your boss finds out you are interviewing. If you are providing value, being a flight risk (within reason) increases your value not decreases. You don't want to be so obviously foot out the door that they are looking for your replacement, but being the happy, uncomplaining soldier is not going to get you optimal raises/promotions.