First off, it’s not recommended to use Cookies in a Capacitor app See Capacitor iOS / Cookie Authentication / capacitor/http.
I am not familiar with STOMP (looks to be a simple text-oriented message protocol over WebSockets), but the way our app is setup with WebSockets, there is a standard HTTPS request that gets sent off first for authorization (the request contains the channel and socket ID). The response returns an auth key to authenticate with the WebSocket server. Is that how your setup is working?
A wild guess is that the Capacitor HTTP plugin isn’t intercepting the WS request so the cookies aren’t getting added to the request.