Thank you! The messages are stored on open-source decentralized messaging backend nodes. (currently there is one run by peakd) The source code is at https://gitlab.com/peakd/sting-message-backend/-/blob/progr-am7/apps/backend/README.md
It has public access and others can start a node and connect to it or start a separate chatting network if they wished.
There is also a js library to communicate with the nodes which can be used read/write messages or listen to new messages on specific channels.
In other words the system is made of 3 modular components:

1. decentralized messaging backend nodes.
2. js library used to communicate with it and for creating, signing, encoding, decoding and verifying messages
3. a frontend and widget implementation using 1. 2.

' 1. 2. still has to have documentation and examples finished before it would be "officially released", however it is already available on the open source repositories.