Visited on June 8 without charging.
The charger is in the public parking. According to the signage, you need to pay for parking like other spots.
Unlike at the Schützenmattweg parking, the maximum park time for the charging station is identical to the general max park time of 2h. However the sign above the charging station doesn't specify any time of day, so it's not clear if the 2h limit also applies on Sunday when regular parking is free and unlimited.