Does geopandas overestimate distances?

You are projecting the data to EPSG:3857, which is a global Mercator projection. Mercator projects the globe to a flat map, retaining angles (useful for marine navigation), but distorting areas and distances more and more the farther they are from the equator. Hence, distances not being correct is to be expected.

The images below illustrate the distortions. The first illustration shows that a distance distortion of +60% is to be expected at ~50° north...

If you want to calculate distances in Europe, you can par example use the equidistant ESRI:102031 projection, which seerms consistent with what you are seeing.

EDIT: I added some more possible projections to the script as well as they were suggested by other users...

import geopandas as gpd
import pandas as pd
autobahn = "A7"
columns = ["ref", "lengthm"]
expecteddistance = 1924
print(f"{autobahn}, expected distance: {expecteddistance} km")
dftotal = pd.DataFrame(columns=columns)
gdf = gpd.readfile(f"https://fliessbaden.de/wp-content/uploads/A7.geojson")
for crs in ["ESRI:102031", "EPSG:25833", "EPSG:32632", "EPSG:4839"]:
    gdf = gdf.tocrs(crs)
    gdf["lengthm"] = gdf.geometry.length
    totalm = gdf['lengthm'].sum()
    totalkm = totalm / 1000
    print(f"{autobahn}, {crs} ({gdf.crs.name}): {str(round(totalkm, 2))} km")

A7, expected distance: 1924 km
A7, ESRI:102031 (EuropeEquidistantConic): 1929.86 km
A7, EPSG:25833 (ETRS89 / UTM zone 33N): 1938.05 km
A7, EPSG:32632 (WGS 84 / UTM zone 32N): 1935.2 km
A7, EPSG:4839 (ETRS89 / LCC Germany (N-E)): 1935.31 km