chore: add microsoft-edge, chromium and brave-origin

Install microsoft-edge on x86_64 Linux via Home Manager and on macOS via
a brew cask. Enable the chromium and brave-origin Home Manager options
alongside google-chrome, dropping the google-chrome aarch64 fallback to
chromium since google-chrome supports aarch64-linux.

Persist the Brave Origin and microsoft-edge profile directories on the
ephemeral-root hosts.

home/linux/gui/base/browsers.nix

@@ -8,8 +8,13 @@
   ];
 
   # source code: https://github.com/nix-community/home-manager/blob/master/modules/programs/chromium.nix
-  programs.google-chrome = {
-    enable = true;
-    package = if pkgs.stdenv.hostPlatform.isAarch64 then pkgs.chromium else pkgs.google-chrome;
-  };
+
+  # open-source upstream Chromium, the base for all the browsers below
+  programs.chromium.enable = true;
+  # the world's most widely used browser, with deep Google account and services integration
+  programs.google-chrome.enable = true;
+  # Brave's privacy-first build (Shields ad/tracker blocking), minus the crypto/AI extras
+  programs.brave-origin.enable = true;
+  # Microsoft's browser, with built-in phishing/malware protection, x86_64 build only
+  programs.microsoft-edge.enable = pkgs.stdenv.hostPlatform.isx86_64;
 }

hosts/idols-ai/preservation.nix

@@ -294,6 +294,8 @@ in
         ".mozilla"
         ".config/google-chrome"
         ".config/chromium"
+        ".config/BraveSoftware/Brave-Origin"
+        ".config/microsoft-edge"
 
         # ======================================
         # CLI data

modules/darwin/apps.nix

@@ -145,6 +145,7 @@ in
       "squirrel-app" # input method for Chinese, rime-squirrel
       "firefox"
       "google-chrome"
+      "microsoft-edge"
 
       "ghostty" # terminal emulator