Is helping an elderly, illiterate man with children by not obliging him to attend work, under the pretext of his presence—knowing that the manager does not ask about him—and accepting a gift from him with the intention of not rejecting him, considered a sin that necessitates repentance, even though the intention was to help this man?

What you did is unlawful unless you were authorized, and the gifts you received are unlawful because they were in exchange for exempting him from work or reducing his workload. Your good intention does not justify what you did. You must repent to Allah and rectify the matter by reinstating the man to his work and informing the relevant authorities of what you did.