If I also use Product FAQs, will the same question appear twice in my search markup?

No. Wcart puts one FAQ block on each product page and merges both sources into it:

• the published FAQs from the Product FAQs plugin
• your quick answers, when FAQ answers in search results (FAQPage) is on in Plugins → AI Search Optimization

If the same question text is in both places, it is listed only once. Answers are sent as plain text. Keep quick answers short and factual, because they are also shown on the page.