Overlaying two LineString doen't get expected result

Question

I have two geodataframe, gdf1 containing the path of a bike route and test containing linestrings of a cycle way :

gdf1 #contains my bike itinerary
>>>  index  length  geometry
     0      1562    LINESTRING (2.33273 48.83389, 2.33267 48.83389...

test
>>>     insee_com   geometry                                            length (meters)
        75114       LINESTRING (2.33666 48.83926, 2.33667 48.83929...   39
        75114       LINESTRING (2.33665 48.83865, 2.33666 48.83926)     68
        75114       LINESTRING (2.33657 48.83969, 2.33658 48.83962)      8

I have mapped those two gdf with plotly express which gives me the following result. We can clearly see the intersection of the two paths :

But I want to have the numerical value of what I see on the map, meaning the length of the intersection of my two paths.

For the moment I tried to use the overlay method but it gives me unexpected results. First it returns me points and multipoints while I was expecting a linestring.

intersection = gpd.overlay(test, gdf1, how = 'intersection', keep_geom_type=False)
intersection.geometry
>>>   0    MULTIPOINT (2.33671 48.83946, 2.33670 48.83940...
      1                             POINT (2.33666 48.83926)
      Name: geometry, dtype: geometry

Second of all, it clearly isn't right on the map...Any help would be really appreciated !