Ok, I feel pretty dumb not to have thought of it before, but I've found the issue.

For the sake of anyone running in the same issue, if you are running an ad blocker, try to disable it first.
Looking at the request in Chromium, it said "ERR_BLOCKED_BY_CLIENT"

Turning off the ad blocker resulted in a dashboard as you would expect it.

Sorry for bothering you for something I should have thought of, and thank you for your support.

I will just leave that here for other like me that wondered for hours why they could flash their sonoff, but it did not react once plugged to the main.

You need to setup your arduino with DOUT as flash mode.
Other mode will flash without errors, but the device will appear bricked.
My settings where:

I'm a bit blind here, but your issue seems to be that you are trying to send a raw float value, without encapsulating it inside a message.
Looking at the example, in the 1.5 version it is:

gw.send(pressureMsg.set(pressure, 0));

Looking at the 1.5 API (http://www.mysensors.org/download/sensor_api_15#MyMessage), creating the message from a float should be

MyMessage& set(float value, uint8_t decimals);

So, you should not use

gw.send (PSI);

but

//declare and init the message
MyMessage msg(BARO_CHILD, V_PRESSURE);
//set it's content
msg.set(PSI,4); //float value with a 4 numbers after decimal precision
//and send the message
gw.send (msg);

Glad I was able to help.