{
            name,
            ...
          }:
let
  inherit (config.flake.modules.x10.device-config.${name}) username;
in
          {
            options.homeManager = {

Something I'd already tried earlier but discarded due to an unrelated error (that I thought told me I could not do things this way):

{
    type =
      with lib.types;
      attrsOf (
        submodule (
          nixosConfig:
          let
            cfg = nixosConfig.config.nixos;
            inherit (nixosConfig.config) hostname username system;
          in
          {
            options.nixos = builtins.break {
              entryPoint = lib.mkOption {
                type = lib.types.path;
                default = "${repoRoot}/nixos/${username}_at_${hostname}";
              };
              toplevelBuild = lib.mkOption {
                type = lib.types.raw;
                readOnly = true;
              };
            };
            config.nixos.toplevelBuild = lib.mkIf (builtins.pathExists cfg.entryPoint) (
              inputs.nixpkgs.lib.nixosSystem {
                modules = [
                  {
                    nixpkgs.hostPlatform = { inherit system; };
                  }
                  (import cfg.entryPoint (inputs // { inherit repoRoot; }))
                  "${repoRoot}/x10/options/unfree-packages.nix"
                  inputs.nur.modules.nixos.default
                ];
                specialArgs = {
                  inherit inputs hostname repoRoot;
                };
              }
            );
          }
        )
      );
  }

So yeah, the inner config variable of the extending submodule contains the submodule's "sibling" option values.

x10an14: taking the discussion from the beginning …

If you want to declare options specific to one instance, you can do it as follow:

{ lib,  ... }@toplevel:
{
  config.flake.modules.foo.<fooInstance> = {config, ...}@submoduleInstance: {
    options.home-manager = lib.mkOption { ... };
    config.home-manager = ...;
  }
}

If you want to make the home-manager option available to all instances, then your initial example is almost there, you have to redefine the foo option with the submodule that you want to add. Submodule option declarations are merged, see fileSystems option as an example, which is declared in multiple modules.

nbp: Thanks! =D

I got it to work, as described in the previous 2x messages of mine =)
This is how I did it: https://git.sr.ht/~x10an14/nix-parts-conf/tree/main/item/device-configs/home-manager.nix

Any feedback/suggestions welcome!
PS: I urge those who've got feedback/suggestions to consider whether it's too niche for this channel/is maybe better suited for a DM =)

Now people might understand why you should not write a NixOS module within a flake, because it lacks position information.

{agenix, ...}:

{
  # Using the module directly prevent the deduplication from working properly.
  imports = [
    agenix.nixosModules.default
  ];
}

Now people might understand why you should not write a NixOS module within a flake.nix file, because it lacks position information.

{agenix, ...}:

{
  # Using the module directly prevent the deduplication from working properly.
  imports = [
    agenix.nixosModules.default
  ];
}