There is no native mechanism in the Genesys Widgets v2.0 to manage this.
The native capability ends the chat when the customer is connected to a Contact Center Agent and no message is sent during 15 minutes.
See Guest Chat APIs page: No activity auto-disconnect While connected to an agent, if the guest does not send any messages for 15 minutes, the guest will be automatically disconnected. This timeout only applies while connected to an agent; activity is not required from the guest while waiting in queue.
You can technically customize the Genesys Widgets (client-side customization).
You could leverage and subscribe to WebChat or WebChatService events (e.g. WebChat.messageAdded or WebChatService.messageReceived) to reset/start your timer.
Upon expiration of your timer, you could request to end the chat (client-side) using WebChat.endChat command or request to add a message in the customer chat live transcript (in the Genesys Widgets UI) using a WebChat.injectMessage command.
See these two answers on another forum post here and here which give some more information on the topic.