In this situation, when entering the tunnel, are you obliged to keep a distance of at least 100 meters from the preceding vehicle?

In the visible situation, you are not required to maintain a distance of at least 100 metres, as there is no B-19 sign "prohibited entry without maintaining distance" with such a value. Sign D-37 only informs about entering a tunnel. According to the general rules set out in Art. 19 para. 2 pt. 3 of the Road Traffic Act, you are obliged to maintain the distance necessary to avoid a collision in the event of braking or stopping of the preceding vehicle.