Set column value based on another columns date

Megaoctane 

Column formatting won't update the values in your other column - it will only allow you to display a value based on some conditions. So if you wanted to actually update the second column's value I believe you'd need to run maybe Power Automate or similar.

If you wanted to just display < 2 months old, etc. in the column and color coded (using pills) then you could do something like the JSON below. In my example I have a column called ApprovalDate of type DateTime and a column called Status of type Single line of text. The long numbers used are milliseconds to get you 4 months (120 days which is 10368000000 milliseconds) and 2 months (60 days which is 5184000000 milliseconds).

The limitations with this are that you won't be able to sort, filter or group by Status as that column doesn't actually contain any values.

{
  "$schema": "https://developer.microsoft.com/json-schemas/sp/v2/column-formatting.schema.json",
  "elmType": "div",
  "style": {
    "flex-wrap": "wrap",
    "display": "flex"
  },
  "children": [
    {
      "elmType": "div",
      "style": {
        "box-sizing": "border-box",
        "padding": "4px 8px 5px 8px",
        "overflow": "hidden",
        "text-overflow": "ellipsis",
        "display": "flex",
        "border-radius": "16px",
        "height": "24px",
        "align-items": "center",
        "white-space": "nowrap",
        "margin": "4px 4px 4px 4px"
      },
      "attributes": {
        "class": {
          "operator": "?",
          "operands": [
            {
              "operator": "<",
              "operands": [
                "[$ApprovalDate]",
                {
                  "operator": "-",
                  "operands": [
                    "@now",
                    10368000000
                  ]
                }
              ]
            },
            "sp-css-backgroundColor-BgCoral sp-css-borderColor-CoralFont sp-css-color-CoralFont",
            {
              "operator": "?",
              "operands": [
                {
                  "operator": "<",
                  "operands": [
                    "[$ApprovalDate]",
                    {
                      "operator": "-",
                      "operands": [
                        "@now",
                        5184000000
                      ]
                    }
                  ]
                },
                "sp-css-backgroundColor-BgGold sp-css-borderColor-GoldFont sp-css-color-GoldFont",
                "sp-css-backgroundColor-BgMintGreen sp-field-borderAllRegular sp-field-borderAllSolid sp-css-borderColor-MintGreenFont sp-css-color-MintGreenFont"
              ]
            }
          ]
        }
      },
      "txtContent": "=if([$ApprovalDate] <= @now - 10368000000, '> 4 months old', if([$ApprovalDate] <= @now - 5184000000, '> 2 months old', '< 2 months old'))"
    }
  ]
}