Spatial join based on polygon centroid in QGIS

You can create a virtual layer with the desired join condition

go to the menu Layer > Add Layer > Add/Edit Virtual Layer... and enter the query

SELECT b.*, p.field1, p.field2
FROM buildings b
JOIN parcels p ON ST_CONTAINS(p.geometry, ST_CENTROID(b.geometry))

Note that it is safer to list the fields of interest from the 2nd layer (parcels) instead of using p.*, as it ensure that the resulting layer contains a single geometry field - from the 1st layer (building).

Another solution based on existing processing algorithms. You can achieve this by doing 2 spatial joins.

1. Extract centeroids via Vector Geometry > Centroids
2. Join the centroids layer with parcels layers, call this centroid_join
3. Join the building footprints layer with centroid join.

It is advisable to explicitly specify the fields in each join, so you don't end up with many duplicate fields.