"having said that" meaning in English

{
  "head_templates": [
    {
      "args": {
        "1": "en",
        "2": "conjunction"
      },
      "expansion": "having said that",
      "name": "head"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "conj",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English deixes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English entries with language name categories using raw markup",
          "parents": [
            "Entries with language name categories using raw markup",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "English terms with non-redundant non-automated sortkeys",
          "parents": [
            "Terms with non-redundant non-automated sortkeys",
            "Entry maintenance"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1826 A Complete Collection of State Trials and Proceedings for High Treason and Other Crimes\nIf I am right in that, the necessary consequence must be that this prisoner must be found guilty; but having said that, let me again request you only to attend to the statement of the law […]"
        }
      ],
      "glosses": [
        "however; despite what one has just stated"
      ],
      "id": "en-having_said_that-en-conj-mKOKUJcn",
      "links": [
        [
          "however",
          "however"
        ]
      ],
      "synonyms": [
        {
          "word": "that being said"
        },
        {
          "word": "that said"
        },
        {
          "word": "nevertheless"
        }
      ]
    }
  ],
  "word": "having said that"
}

{
  "head_templates": [
    {
      "args": {
        "1": "en",
        "2": "conjunction"
      },
      "expansion": "having said that",
      "name": "head"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "conj",
  "senses": [
    {
      "categories": [
        "English conjunctions",
        "English deixes",
        "English entries with incorrect language header",
        "English entries with language name categories using raw markup",
        "English lemmas",
        "English multiword terms",
        "English terms with non-redundant non-automated sortkeys"
      ],
      "examples": [
        {
          "text": "1826 A Complete Collection of State Trials and Proceedings for High Treason and Other Crimes\nIf I am right in that, the necessary consequence must be that this prisoner must be found guilty; but having said that, let me again request you only to attend to the statement of the law […]"
        }
      ],
      "glosses": [
        "however; despite what one has just stated"
      ],
      "links": [
        [
          "however",
          "however"
        ]
      ]
    }
  ],
  "synonyms": [
    {
      "word": "that being said"
    },
    {
      "word": "that said"
    },
    {
      "word": "nevertheless"
    }
  ],
  "word": "having said that"
}