Hello @jlejeune, great question. There are a few attribute/property changes from the previously named "start" and "end" attributes to "value" or "valueAsDate".
For Date Pickers with "range", an array of date strings can be added to the component, where the array is added via JavaScript (non-range examples can be modified with the attribute in HTML).
For instance, see the code below, also in this Codepen sample:
<calcite-date-picker id="calendar" range proximity-selection-disabled scale="s" max="2500-01-01" min="1900-01-01"></calcite-date-picker>
<script>
document.querySelector("calcite-date-picker").value = ["2021-01-01", "2021-01-02"];
</script>