You can join them, then select the rows which are not in the join.
Find the features in df that are not intersecting df2:
import geopandas as gpd
df = gpd.read_file(r"C:/GIS/data/Bakgrundskartor/Topografi_250/data/mark_sverige.gpkg", layer="sankmark")
df["tempid"] = range(0, df.shape[0]) #Create an id column
df2 = gpd.read_file(r"C:/GIS/data/Bakgrundskartor/Topografi_250/data/naturvard_sverige.gpkg", layer="skyddadnatur")
joined = gpd.sjoin(left_df=df, right_df=df2, how="inner", predicate="intersects") #Find the intersecting polygons
nonintersecting = df.loc[~df["tempid"].isin(joined["tempid"])] #Select the ids in df, that are not in the spatial join output
