Germans call it Schaumstoff (foam) Formteil (molding) ohne Teppich (without carpet): https://mbzclassicparts.com/en/collections/gummimatten/products/w123-s123-sedan-t-modell-schaumstoff-formteil-set-vierteilig-neu

which doesn't seem too far off from what I call it... "that foam stuff on the bottom of the carpet floor mats".

I think my main question is whether anyone is aware of where this might be sold stateside?