To connect to Groq, please make sure that you have a GroqCloud account (https://console.groq.com/).
While there is no native connection to Groq inside Novelcrafter, they support the "OpenAI" standard, so you just need to do the following:
Create a new "OpenAI" connection
Rename the connection to "Groq"
Enter your API key from Groq (generate a new one here: https://console.groq.com/keys)
Enter the following as the Base URL: https://api.groq.com/openai/v1
If everything works, you should see the models appear: