System Wide Remap

{
    "description": "Cmd+D / Cmd+E → Ctrl+Tab / Ctrl+Shift+Tab",
    "manipulators": [
        {
            "from": {
                "key_code": "d",
                "modifiers": {
                    "mandatory": ["command"],
                    "optional": ["any"]
                }
            },
            "to": [
                {
                    "key_code": "tab",
                    "modifiers": ["left_control"]
                }
            ],
            "type": "basic"
        },
        {
            "from": {
                "key_code": "e",
                "modifiers": {
                    "mandatory": ["command"],
                    "optional": ["any"]
                }
            },
            "to": [
                {
                    "key_code": "tab",
                    "modifiers": ["left_control", "left_shift"]
                }
            ],
            "type": "basic"
        }
    ]
}

Zen Specific Remap

{
  "description": "Cmd+D / Cmd+E → Ctrl+Tab / Ctrl+Shift+Tab in Zen only",
  "manipulators": [
    {
      "conditions": [
        {
          "type": "frontmost_application_if",
          "bundle_identifiers": [
            "app.zen-browser.zen"
          ]
        }
      ],
      "from": {
        "key_code": "d",
        "modifiers": {
          "mandatory": ["command"],
          "optional": ["any"]
        }
      },
      "to": [
        {
          "key_code": "tab",
          "modifiers": ["left_control"]
        }
      ],
      "type": "basic"
    },
    {
      "conditions": [
        {
          "type": "frontmost_application_if",
          "bundle_identifiers": [
            "app.zen-browser.zen"
          ]
        }
      ],
      "from": {
        "key_code": "e",
        "modifiers": {
          "mandatory": ["command"],
          "optional": ["any"]
        }
      },
      "to": [
        {
          "key_code": "tab",
          "modifiers": ["left_control", "left_shift"]
        }
      ],
      "type": "basic"
    }
  ]
}