Does anybody know how to only label features of a shapefile that are inside of another shapefile's features used as coverage in Atlas?
For your case, that the current layer and the coverage layer don't share a similar field, you will need to use the following rule:
If the current layer and the coverage layer share a similar field, then you can use:
"my_filed" = attribute(@atlasfeature, 'atlas_similar_field_name')
Finally, if the layer you want to filter is the coverage layer, then you can use this one:
$id = @atlas_featureid