If I want to use api-gateway + lambda as my API backend, I feel a Next.js app is slower than CRA app, but people disagree, what am I missing

I think a next.js app is fundamentally slower than a CRA app, why am I wrong /right on this thought? (I am taking about a serverless deployment scenario)

For a CRA created app, it is understandable that the customer gets the first meaningful page slower than the the one from next.js app
— the reason is that a CRA app serves all page assets upfront, but next.js just serves one page

However, after the first page is served, all the other page rendering become the following 2 steps for a CRA app:
1. Browser makes an api calls to the API server;
2. Browser render the page by filling the JSON served from step 1.

For the next.js app though, the process is more expensive in my opinion:

1. Browser makes a full page call to the page serving endpoint (say it is an AWS CloudFront edge endpoint or vercel endpoint);
2. Browser further make an API call to the API server, or the page serving server makes an API call to the API server (btw, I don’t know which is the case — but certainly it is another round of network traffic)
3. Only after the above two steps, can a page is fully rendered

But for a CRA app, step 1 has been down upfront when loading the app (and that’s why the first meaningful page is slow)

So we can clearly see next.js need more time to render a page such as ‘/dashboard’.

Can someone explain to me why people think next.js is more performant than a CRA app?

PS: I am not arguing the value next.js provides such as SEO friendliness; I just want to make sure I understand the performance side of the story clearly