In short, the answer is no. Next.js is not a product of Facebook, although it is heavily influenced by the company. The original creator of Next.js, Zeit, is an independent company that was founded in 2015 and is not affiliated with Facebook.
The React Server Components library has become a core part of the Next.js framework. In 2020, Facebook also acquired Vercel, the company behind Next.js, further solidifying the relationship between the two.
In conclusion, Next.js is not a product of Facebook. The framework was created by Zeit and is now owned by Vercel. However, Facebook has played an important role in the growth of Next.js, open-sourcing the React Server Components library and acquiring Vercel in 2020.