Uncaught InvalidStateError: Failed to execute ‘send’ on ‘WebSocket’: Still in CONNECTING state

You could send messages via a proxy function that waits for the readyState to be 1.

this.send = function (message, callback) {
    this.waitForConnection(function () {
        ws.send(message);
        if (typeof callback !== 'undefined') {
          callback();
        }
    }, 1000);
};

this.waitForConnection = function (callback, interval) {
    if (ws.readyState === 1) {
        callback();
    } else {
        var that = this;
        // optional: implement backoff for interval here
        setTimeout(function () {
            that.waitForConnection(callback, interval);
        }, interval);
    }
};

Then use this.send in place of ws.send, and put the code that should be run afterwards in a callback:

this.ident = function () {
    var session = "Test";
    this.send(session, function () {
        window.identified = true;
        theText.value = "Hello!";
        say.click();
        theText.disabled = false;
    });
};

For something more streamlined you could look into promises.