Reproducing a bug in Vercel.
If you have just Next.js in the ./ui directory and deploy it, both static and dynamic routes work. Once you add the Python Flask app in ./api only the dynamic routes no longer work.
This is despite Vercel showing the successful Next.js output listing both routes:
18:23:18.932 $ next build ./ui
18:23:19.640 info - Creating an optimized production build...
18:23:22.801 info - Compiled successfully
18:23:22.801 info - Collecting page data...
18:23:22.855 info - Generating static pages (0/1)
18:23:23.089 info - Generating static pages (1/1)
18:23:23.089 info - Finalizing page optimization...
18:23:23.099 Page Size First Load JS
18:23:23.099 ┌ ○ /404 2.77 kB 65.7 kB
18:23:23.099 ├ λ /api/[dynamic] 0 B 63 kB
18:23:23.099 └ λ /api/static 0 B 63 kB
18:23:23.099 + First Load JS shared by all 63 kB
18:23:23.099 ├ chunks/commons.b298e0.js 13 kB
18:23:23.099 ├ chunks/framework.b5c8be.js 41.9 kB
18:23:23.099 ├ chunks/main.0bf900.js 6.24 kB
18:23:23.099 ├ chunks/pages/_app.6b425e.js 1.01 kB
18:23:23.099 └ chunks/webpack.e06743.js 751 B
18:23:23.100 λ (Lambda) server-side renders at runtime (uses getInitialProps or getServerSideProps)
18:23:23.100 ○ (Static) automatically rendered as static HTML (uses no initial props)
18:23:23.100 ● (SSG) automatically generated as static HTML + JSON (uses getStaticProps)
18:23:23.100 (ISR) incremental static regeneration (uses revalidate in getStaticProps)
18:23:23.180 Done in 4.27s.
On the Python side, Vercel doesn't mention anything it's doing with the Flask app other than:
18:23:26.304 Installing build runtime...
18:23:27.940 Build runtime installed: 1635.298ms
18:23:28.326 Looking up build cache...
18:23:28.363 Build cache not found
18:23:28.751 Installing required dependencies...
18:23:36.355 Uploading build outputs...
18:23:39.355 Done with "api/app.py"
And it doesn't appear to be accessible at any routes.