If you look at the official ArcGIS example at https://developers.arcgis.com/calcite-design-system/components/split-button/, you'll see that structure of button is completely different from what are you trying with your code.
Here is the structure from the example:
<calcite-split-button primary-text="Add a vegetable">
<calcite-dropdown-group selection-mode="none" group-title="Recently added">
<calcite-dropdown-item>Pea</calcite-dropdown-item>
<calcite-dropdown-item>Parsnip</calcite-dropdown-item>
<calcite-dropdown-item>Radish</calcite-dropdown-item>
<calcite-dropdown-item>Tomato</calcite-dropdown-item>
<calcite-dropdown-item>Rutabaga</calcite-dropdown-item>
<calcite-dropdown-item>Bean</calcite-dropdown-item>
</calcite-dropdown-group>
</calcite-split-button>
To create this kind of a structure with JS code, it should look something like this:
let calciteBtn = document.createElement("calcite-split-button");
calciteBtn.setAttribute('primary-text', 'Run Screening Tool');
calciteBtn.setAttribute('dropdown-icon-type', 'ellipsis');
calciteBtn.setAttribute("primary-icon-start", "analysis");
let calciteGroup = document.createElement("calcite-dropdown-group");
calciteGroup.setAttribute('selectionMode', 'single"');
calciteBtn.appendChild(calciteGroup);
let calciteItem1 = document.createElement("calcite-dropdown-item");
calciteItem1.innerHTML = 'Run Tool and save report.';
calciteGroup.appendChild(calciteItem1);
let calciteItem2 = document.createElement("calcite-dropdown-item");
calciteItem2.innerHTML = 'Run Tool and save report.';
calciteGroup.appendChild(calciteItem2);
document.getElementById('body').appendChild(calciteBtn);
That's how it looks like then: