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

You can inner join the dataframes, then select the rows that 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