You can aggregate the geometries of each layer and than combine them using collect_geometries(). The final expression could look like this - replace 'poly1', 'poly2' etc. with the names of your polygon layers:

collect_geometries( 
aggregate( 'poly1','collect',$geometry),
aggregate( 'poly2','collect',$geometry),
aggregate( 'poly3','collect',$geometry)
)

Screenshot 1: original polygons (3 layers):

Screenshot 2: the collected polygons with a common line-pattern:

You can aggregate the geometries of each layer and than combine them using collect_geometries(). The final expression could look like this - replace 'poly1', 'poly2' etc. with the names of your polygon layers:

collect_geometries( 
    aggregate('poly1', 'collect', $geometry),
    aggregate('poly2', 'collect', $geometry),
    aggregate('poly3', 'collect', $geometry)
)

Screenshot 1: original polygons (3 layers):

Screenshot 2: the collected polygons with a common line-pattern: