The next.js method is completely static. You can run your wordpress instance locally in your laptop/pc, run next.js static site generator, then upload the resulting static site to aws or github pages. No need to run the wordpress instance 24/7 as it's only required as a data source during static site generation and can be turned off when you're done with it.

There is also an option in cloudflare to pre-cache everything on their edge servers so visitors will never hit the origin server, but it's not available in free plan (I think it's enterprise only plan).