Chatwoot is an open-source self-hosted live chat software. Besides their website chat integration, they offer an omnichannel panel that enables you to handle all customer requests from different platforms (website, email, social media, WhatsApp) from a centralized standpoint. Messages can be automatically tagged or assigned to people based on certain triggers, e.g., detecting the language of the message and assigning it to someone who speaks that language, or they can be answered by a customizable chatbot.

The self-hosting documentation can be accessed here.