OpenAI rewrote its help page as 'Shopping with ChatGPT Search'. It now says that when several merchants sell a product, it ranks them on factors like availability, price, quality and whether they're the maker or primary seller. It also highlights the lowest price it knows of with a 'Best price' label.
Shopify merchants' product data already reaches ChatGPT through Shopify Catalog. Other merchants can apply for a direct feed. ChatGPT may also write its own simplified titles, descriptions and labels.
That last part matters. If ChatGPT rewrites your product copy, the cleaner your source data, the closer its version stays to yours.