What is the ruling on a reciprocal emotional relationship between a young man and a woman via messages when they both desire marriage but cannot complete it currently, and how can this relationship be maintained in a religiously permissible manner until marriage, while ensuring the acceptance of their repentance?

Your relationship with this girl—messaging her and dating her—is impermissible. The only legitimate Islamic way is marriage. If you are unable to marry, then you must sever the relationship. According to Sheikh Ibn Uthaymeen, the Islamic way to deal with affection between a man and a woman who are not married is for him to propose to her and marry her with a valid nikah. It is not permissible to contact her privately before the contract, or to exchange love messages, because this causes fitna (temptation/strife). If you repent to Allah with a sincere repentance, then repentance is accepted.