The chat can be started either by pressing the main Chat icon or the Chat icon in the Heard Stations list.
To send a message to a station not in the Heard Stations List, press the Chat icon and fill in the callsign with/without SSID, the message and then press Start a new chat.
To reply/read to a previously received/transmitted message press the Chat icon.
You should now see a list with the stations you have send/received messages to/from. Select the callsign, fill in the message and/or add icons/attachment and press send.
Firefox 129.0 64bit on Ubuntu 22.04.4 LTS the file requester for attachments doesn't work. Maybe a popup settings? Please report back.