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

Why?

The visible D-37 sign indicates a tunnel, but does not itself require a 100 m gap. You must keep enough distance to avoid a collision if the vehicle ahead brakes. For a passenger car without a trailer, a minimum gap of 50 m applies in tunnels longer than 500 m outside built-up areas, unless signs specify otherwise.

Art. 19 ust. 2 pkt 3 oraz ust. 4 i 5 Prawa o ruchu drogowym