In some sense "squishy" is a good description of how we design cars, you want the car to squish in a collision to avoid rattling the people around too forcefully.

QQ is actually just pronounced like QQ in English. If I remember correctly, it was first popularized by a type of candy - call QQ candy, which I think is where the soft and squishy meaning the OP referred to came from.

Next was QQ the software, I think inspired by the name ICQ, developed by WeChat's developer, Tencent. Prior to smart phones and wechat - QQ was the dominating platform