Shared e-scooters are emerging as a key component of sustainable urban mobility, offering flexible solutions for first- and last-mile travel. This study investigates the integration of shared e-scooters with public transportation in Gothenburg, Sweden, where formal regulations and planning strategies are still evolving. Using clustering analysis and point-of-interest (POI) data, we identify patterns of multimodal connectivity between e-scooters and public transport stops. Our findings reveal that approximately 20% of e-scooter trips are functionally integrated with public transit, split equally between first- and last-mile connections, while the remaining 80% are non-integrated. Integration rates are highest in areas with dense transit infrastructure, such as central Gothenburg and multimodal hubs like Stenpiren, where POI density, service efficiency, and e-scooter availability converge. Commuters are generally willing to walk up to 1 km to reach an e-scooter when connections are convenient and reliable. These results underscore the need for coordinated micromobility and transit planning to enhance system-wide accessibility and promote sustainable travel behavior in urban contexts.