Embeddable automatically applies a z-index to every component on the canvas. This means that you can add additional components (e.g. tooltips, dropdowns, etc.) as long as they expand downwards - but not sideways or upwards. This is because z-indexes are lower as you go down the page.
If you want to add a component that opens as a new modal for example, to work around this, you could use the variable listener on the embedded web component (see Embedding an Embeddable in the handbook). That way you could listen to the appropriate variable change, and then open a modal in your react app, on top of the Embeddable dashboard.