Problem with spatial join of large shapefiles

I want to combine the attributes of five shapefiles into one shapefile using QGIS. Therefore, I used several data processing steps including clipping the five shapefiles to the boundaries of my investigation area using Vector > Geoprocessing Tools > Clip and using Fix Geometries to avoid invalid polygons. The polygon shape and number of the shapefiles are different, but they have the CRS.

I used Vector > Data Management Tools > Join Attributes by location to join the shapefiles.
But after I joined the third shapefile, the shapefile size has already reached around 1 GB. I have read that the maximum shapefile size is 2 GB. While joining the fourth shapefile, the computation time was really long and my computer crashed around half of it. I tried it a second time, but it happened again.

My three shapefiles look like this:

1. Temperature_Precipation_Slope with 40.423 Features
   (already joined three shapefiles)

Field       Type      Length     Precision
Precipitat  Integer   4          0
Temperatur  Integer   2          0
Slope       Integer   1          0

2. BUEK200 with 101 features

Field       Type      Length     Precision
TKLE_NR     Integer   6          0

3. CLC10 with 2675 features

Field       Type      Length     Precision
clc         Integer   3          0

I already decreased and aggregated my data, by using ranges in the attribute tables to minimize the number of polygons within one shapefile. Moreover, I changed the type and size of the fields with Refactor fields.

I could add the fourth shapefile and save it as a GeoPackage, but the size of the GeoPackage was already 17 GB.
While adding the fifth shapefile and saving the result as a GeoPackage, my laptop crashed again. I guess I don’t have enough memory space to save such a large file.

I now try to use PostGIS (which I haven’t used before) and managed to upload my shapefiles into the two tables Temperature_Precipation_Slope and Buek200_CLC10.

If I understood correctly I can’t use ST_Union, as the shapefiles don’t have a common attribute.

SELECT * From "Temperature_Precipation_Slope"
SELECT * From "Buek200_CLC10"

However, I don’t understand how to perform the spatial join by location

CREATE TABLE gis_data AS
SELECT tps.precipitat, tps.temperatur, tps.slope, bc.tkle_nr, bc.clc
From "Temperature_Precipation_Slope" tps, "Buek200_CLC10" bc
WHERE ST_Intersects(tps.geom, bc.geom);