OH3 graph in Card/Widget?

Not quite. The complete code from one of the chart pages that you build in the chart editor needs to be in an oh-chart component which itself is best served if it’s on something else with a background such as a card.

Chart card example yaml
component: f7-card
config: {}
slots:
  default:
    - component: oh-chart
      config:
        chartType: ""
        period: D
        label: Full Temperature Tracking
      slots:
        grid:
          - component: oh-chart-grid
            config:
              includeLabels: true
        xAxis:
          - component: oh-time-axis
            config:
              gridIndex: 0
        yAxis:
          - component: oh-value-axis
            config:
              gridIndex: 0
              name: °F
          - component: oh-value-axis
            config:
              gridIndex: 0
        series:
          - component: oh-time-series
            config:
              name: Master Bedroom
              gridIndex: 0
              xAxisIndex: 0
              yAxisIndex: 0
              type: line
              item: Sensor_MasterBedroom_Temperature
        tooltip:
          - component: oh-chart-tooltip
            config:
              confine: true
              smartFormatter: true
        legend:
          - component: oh-chart-legend
            config:
              bottom: 3
              type: scroll
        dataZoom:
          - component: oh-chart-datazoom
            config:
              type: inside

I think you are correct though that this require one of the 3.1 versions, though I can’t say for sure.