I use Discord for notifications when someone starts a "Chat with customer support" chat on my site. I tried various "chat button" solutions, but I ended up writing the chat system myself because no solution was really tailored to my task (esp. custom file type uploads and Google Ads integration, so I know which ad started a chat). I need to react 24/7 to new customers, so I needed a tool to ping me with notifications on my phone. The chat messages are still saved in the company database, but I send a link with the Chat ID to Discord, so that someone can instantly login to the admin panel and reply to the customer.
Using Discord, all I had to do was to create a new, empty company server, copy the webhook URL and then POST to the URL and boom I get a ping notification with the Chat ID on my phone (or I can @ a colleague to distribute the customer support for different timezones).
It's not a very "orthodox" solution, but it certainly sucks less than the alternatives (plus it's free).