Looks like you have the remains of an aftermarket steel center cap corroded in place. I bet if you knock that out of the wheel, a traditional (oem plastic) center cap will fit just fine. But if you need to find the outer part of an aftermarket cap to match what you have on the other wheels - that may not be easy.
I'd go ahead and splurge on a set of one of the oem variants for your "new" car; they all hold up pretty well, except that the ones with a colored Porsche crest will have clouding of clear over the crest after a few years of UV exposure. The ones without the circumferential groove, while technically not "correct" for your year, are easier to clean and look good.
BOL
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