Here's the simple solution I'm using with Karabiner Elements to map Fn keys in VS Code. It doesn't support using Fn+F keys to do media functions within VS Code - I may fiddle more to add that if it gets annoying.

{
            "description": "VS Code Function keys work as Fn keys",
            "manipulators": [
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f1",
                  "modifiers": {
                    "optional": ["any"]
                  }
                },
                "to": [
                  {
                    "key_code": "f1"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f2"
                },
                "to": [
                  {
                    "key_code": "f2"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f3"
                },
                "to": [
                  {
                    "key_code": "f3"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f4"
                },
                "to": [
                  {
                    "key_code": "f4"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f5"
                },
                "to": [
                  {
                    "key_code": "f5"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f6"
                },
                "to": [
                  {
                    "key_code": "f6"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f7"
                },
                "to": [
                  {
                    "key_code": "f7"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f8"
                },
                "to": [
                  {
                    "key_code": "f8"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f9"
                },
                "to": [
                  {
                    "key_code": "f9"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],

                "from": {
                  "key_code": "f10"
                },
                "to": [
                  {
                    "key_code": "f10"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f11"
                },
                "to": [
                  {
                    "key_code": "f11"
                  }
                ],
                "type": "basic"
              },
              {
                "conditions": [
                  {
                    "file_paths": ["Visual Studio Code\\.app"],
                    "type": "frontmost_application_if"
                  }
                ],
                "from": {
                  "key_code": "f12"
                },
                "to": [
                  {
                    "key_code": "f12"
                  }
                ],
                "type": "basic"
              }
            ]
          }