Is it obligatory to accept a marriage proposal from a man of good character and religious commitment, according to the Hadiths of the Prophet, peace and blessings be upon him, or is it permissible to refuse for someone who does not desire marriage and fears depression because of it?

Your fear is exaggerated. Marriage in Islam is not perpetual; rather, Allah has provided an exit when cohabitation becomes impossible. Furthermore, your acceptance of a man of good character and religious commitment is a blessing. Marriage is a fortress against temptations and desires, and some scholars deem it obligatory for those who fear temptation, or for every capable person who has desires, and that a woman must accept a suitable husband. Sheikh Ibn Uthaymeen and Sheikh Ibn Baz have affirmed the obligation of marriage for every capable person, due to the great benefits it entails, such as chastity of the private parts, lowering the gaze, and increasing the Muslim nation.