All direct messages and group chats on insteady are end-to-end encrypted. This means only you and your conversation partner can read the content. insteady has no access to your messages.
When you first open Messages, cryptographic keys are generated on your device. Your private key never leaves your device. Only the public key is shared with insteady, so others can send you encrypted messages.
Your keys are stored in your browser's local storage. If you clear your browser data or use a new device, you will not be able to decrypt older messages without your encryption recovery code.
Under Settings - Encryption recovery code you will find your personal recovery code. Store it securely - for example in a password manager. It lets you restore your messages on a new device or after clearing browser data.