Remote functions: endpoint is inaccessible when deploying via Netlify adapter with edge config

[nickbreaton]

Describe the bug

When deploying remote functions to Netlify via the @sveltejs/netlify-adapter with { edge: true } configured, remote functions fail to load due to a 404 response from the server.

Reproduction

This repository contains the issue as minimal reproduction:
https://github.com/nickbreaton/svelte-kit-netlify-adapter-repro

The commit log may be helpful, but specifically the commit 175ae9 is deployed to a Netlify project which can be found at the permalink here:
https://689def082aaba60008a349b2--svelte-kit-netlify-adapter-repro.netlify.app/

Logs

GET https://689def082aaba60008a349b2--svelte-kit-netlify-adapter-repro.netlify.app/_app/remote/19aeq9f/getRemoteData 404 (Not Found)

System Info

System:
    OS: macOS 15.6
    CPU: (8) arm64 Apple M1 Pro
    Memory: 992.63 MB / 32.00 GB
    Shell: 5.9 - /bin/zsh
  Binaries:
    Node: 24.4.1 - /opt/homebrew/bin/node
    npm: 11.4.2 - /opt/homebrew/bin/npm
    pnpm: 8.6.3 - /opt/homebrew/bin/pnpm
    bun: 1.2.20 - ~/.bun/bin/bun
  Browsers:
    Chrome: 139.0.7258.68
    Chrome Canary: 141.0.7354.0
    Safari: 18.6
    Safari Technology Preview: 26.0
  npmPackages:
    @sveltejs/adapter-auto: ^6.1.0 => 6.1.0 
    @sveltejs/adapter-netlify: ^5.1.1 => 5.1.1 
    @sveltejs/kit: ^2.30.0 => 2.30.0 
    @sveltejs/vite-plugin-svelte: ^6.1.2 => 6.1.2 
    svelte: ^5.38.1 => 5.38.1 
    vite: ^7.1.2 => 7.1.2

Severity

annoyance

Additional Information

I've taken a stab at fixing in #14214