Does the feeling of longing to commit a sin while seeking forgiveness and repenting from it constitute false seeking of forgiveness and repentance?

As long as you are refraining from sin and determined not to return to it, your seeking forgiveness (istighfar) and repentance (tawbah) are valid. The inclination of the soul towards sin does not harm as long as you struggle against it and deter it. This inclination is dangerous and can affect the sincerity of repentance, and it might cause you to return to sin. Whoever still finds the sweetness of sin in their heart or looks upon it with thought, there is a fear that they will return to it, except through intense struggle and aversion towards it. Among the signs of suspecting the repentance is weakness of resolve, the heart's turning back to sin, and remembering the sweetness of its commission. Therefore, strive to detest sin and bring to mind its harm to your religion to help you loathe it and prevent your heart from turning to it.