Thank you all for the replies.
Earlier today I went to a Toyota authorised body repair shop (is this the right term?) to have the issue checked. They told me that the wetness of the specific spot must be due to water coming from shoes (inside the car), as the rest of the floor was not wet. As regards the soft spots (there are more than one, as I realised by feeling it with bare hands), they told me that this is normal. I told them that this is prone to tearing after some time - e.g. the space between the door and the brake is really soft and there seems to be no metal underneath it - but they assured me that this is not going to happen.
I still find it confusing that none of you confirmed the same structure of the driver's floor; does it really feel homogeneous (e.g. no soft spots)? Mine feels like there are wide rods below the fabric, which are not exactly fit one next to the other...
I'll have the issue checked by my car dealer (where I got the car from) in the next days, where I'll ask for the thorough check of the car, including the specific spot.