fix: anilist auth failed to open link on Windows

Switches to using the standard web browser module for opening the authentication URL, providing clearer feedback to the user about browser launch success or failure.

fastanime/cli/commands/anilist/commands/auth.py

@@ -1,4 +1,5 @@
 import click
+import webbrowser
 
 from .....core.config.model import AppConfig
 
@@ -41,9 +42,14 @@ def auth(config: AppConfig, status: bool, logout: bool):
             return
     api_client = create_api_client("anilist", config)
 
-    # TODO: stop the printing of opening browser session to stderr
-    click.launch(ANILIST_AUTH)
-    feedback.info("Your browser has been opened to obtain an AniList token.")
+    open_success = webbrowser.open(ANILIST_AUTH, new=2)
+    if open_success:
+        feedback.info("Your browser has been opened to obtain an AniList token.")
+        feedback.info(f"or you can visit the site manually [magenta][link={ANILIST_AUTH}]here[/link][/magenta].")
+    else:
+        feedback.warning(
+            f"Failed to open the browser. Please visit the site manually [magenta][link={ANILIST_AUTH}]here[/link][/magenta]."
+        )
     feedback.info(
         "After authorizing, copy the token from the address bar and paste it below."
     )