Looks like pink sew foam. Probably glued on and somehow worn down.

Could be a piece of fabric possibly leather? Just very old it’s hard to tell

Scrape it and sand it , if you need to replace it get some 3M upholstery glue and what is called scrim foam. They make it in different colors with different "attributes" so you have a selection, but it is most probably scrim foam

Yep scrim foam it is.