I found out that the issue is not with augmenting #app module but with .nuxt/tsconfig.json
included files.
For instance for the @sidebase/nuxt-auth
path, we have with yarn
../node_modules/@sidebase/nuxt-auth/runtime
but it should be ../node_modules/@sidebase/nuxt-auth/dist/runtime
. I see that a lot of includes are missing that dist
folder.