Is a conversation between a female supervisor and a male forum moderator in a work context considered unlawful khalwa (private seclusion between a man and a woman who are not mahram)?

There is no religious impediment for a woman to speak with a non-mahram (definition) man, whether from her relatives or others, for reassurance or for any purpose, either directly or through communication channels, provided that she adheres to religious etiquette and avoids seclusion (khalwa (definition)) or being soft in speech. Indeed, the Companions used to speak with women. It is permissible for a woman to consult people of experience and specialization in her religious and worldly affairs, as long as it is within the bounds of Islamic law and etiquette. Speaking with a non-mahram is not forbidden in itself as long as sedition (fitna) is secure and religious etiquette is adhered to. It is only forbidden if it involves something unlawful or leads to it.