I’ve used lead quite a bit for various things. It’s “soft” for a metal, but it is nothing like clay and is not “squishy”. It is relatively easily bent and will take a rubber hammer to easily form to shapes. I really can’t think of a material one would encounter in daily use that is comparable to the malleability of lead. So “very soft”, yes, but it is metal.
I've never heard it compared to clay but yeah it does make sense. Lead flashing is probably a little bit thicker than what you have and it's very pliable, it can easily be shaped with just one finger, I can definitely see how it could be called squishy.