bug: VSCode profiles get overriden on first launch

[Toby222]

Are you following the right branch?

• My Nixpkgs and Home Manager versions are in sync

Is there an existing issue for this?

• I have searched the existing issues

Issue description

With the addition of profile support with #5640, I noticed that the first iteration of profile configs gets overriden when I launch VSCodium for the first time.
Subsequently rebuilding the profiles puts them back and VSCode doesn't delete them, leading me to think that HM is missing some marker to show that the files should stay there?

Maintainer CC

No response

System information

- system: `"x86_64-linux"`
 - host os: `Linux 6.12.16, NixOS, 25.05 (Warbler), 25.05.20250224.0196c01`
 - multi-user?: `yes`
 - sandbox: `yes`
 - version: `nix-env (Lix, like Nix) 2.91.1
System type: x86_64-linux
Additional system types: i686-linux, x86_64-v1-linux, x86_64-v2-linux, x86_64-v3-linux, x86_64-v4-linux
Features: gc, signed-caches
System configuration file: /etc/nix/nix.conf
User configuration files: /home/toby/.config/nix/nix.conf:/etc/xdg/nix/nix.conf:/home/toby/.nix-profile/etc/xdg/nix/nix.conf:/nix/profile/etc/xdg/nix/nix.conf:/home/toby/.local/state/nix/profile/etc/xdg/nix/nix.conf:/etc/profiles/per-user/toby/etc/xdg/nix/nix.conf:/nix/var/nix/profiles/default/etc/xdg/nix/nix.conf:/run/current-system/sw/etc/xdg/nix/nix.conf
Store directory: /nix/store
State directory: /nix/var/nix
Data directory: /nix/store/zm68nasdmai8qzgzlb55m10mrl93dzqd-lix-2.91.1/share`
 - nixpkgs: `/nix/store/593xvgv994xlkm5mb7w4p1xxnzrs9wv6-source`