Svelte example from main doesn't work

[PerchunPak]

Environment

  System:
    OS: Linux 6.13 cpe:/o:nixos:nixos:25.05 25.05 (Warbler)
    CPU: (12) x64 AMD Ryzen 5 5500U with Radeon Graphics
    Memory: 3.08 GB / 14.96 GB
    Container: Yes
    Shell: 3.7.1 - /run/current-system/sw/bin/fish
  Binaries:
    Node: 22.12.0 - ~/.nix-profile/bin/node
    npm: 10.9.0 - ~/.nix-profile/bin/npm
    pnpm: 10.2.0 - ~/.nix-profile/bin/pnpm
    bun: 1.2.2 - ~/.nix-profile/bin/bun
    Watchman: 2025.01.06.00 - /home/perchun/.nix-profile/bin/watchman
  Browsers:
    Chromium: 132.0.6834.159
  npmPackages:
    @auth/kysely-adapter: ^1.7.4 => 1.7.4 
    @auth/sveltekit: ^1.7.4 => 1.7.4 

Reproduction URL

https://github.com/nextauthjs/next-auth/tree/main/apps/dev/sveltekit

Describe the issue

see below

How to reproduce

lox.mp4

Expected behavior

authorization would work, becuase cookie wouldn't be removed

[PerchunPak]

The example I refer to is https://github.com/nextauthjs/next-auth/tree/main/apps/dev/sveltekit