Welcome to the forums @Costas2021,
First, the tutorial is showing the on-line editor PhotoPea. This generally shouldn't be important, however becomes important due to how it treats the SVG file. As you can see in the tutorial the SVG file has many Groups.
Did you download the SVG format or PNG? If the latter, then there's nothing but a flattened pixel layer, no groups or Layers. Different programs treat the layers/groups differently. Affinity Designer treated them as Layer-Layers not Group-Layers.
So since they are not Groups, there is not a short-cut command to ungroup them. I'm not very well versed in Designer, but all the searching I've done, reveals that the only way to ungroup the Layer-groups is to open them, select all the sub-layers, then drag them out of the layer-group.
I watched some of the tutorial, and if you're just wanting to remove the color, there's really no need to ungroup. Just open the layer, select all the sub-layer, can be done by selecting the first sub-layer, not the one labeled Layer, then holding down Shift and selecting the last one. Then go to the Color Panel and selecting the color, which the tutorial states White. That's what I'd do, instead of ungrouping them. In fact, unless PhotoPea doesn't allow it, even if they're grouped, I would just leave them grouped, much easier to manage.