Is the heart's inclination towards an unseen person and preoccupation with thoughts of them, along with scholarly correspondence containing allusions from them, considered a form of "zina of the heart" (adultery of the heart) and deserving of sin, especially since the person is married?

It is not permissible to correspond with foreign men online except out of necessity and with controls, because it may be a gateway to fitna (temptation) and an enticement by Satan. A woman's mere inclination towards a man is not problematic as long as it does not lead to something forbidden. A person is not held accountable for inner thoughts, but dwelling on thoughts is a gateway to fitna and corruption. It is obligatory to guard thoughts and not dwell on them, because they are the seeds of Satan and the self. It is permissible for a woman to offer herself in marriage to a righteous man, with controls and etiquette.