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

There is no general 100 m requirement here. Keep enough distance to avoid a collision. In a tunnel longer than 500 m outside a built-up area, the minimum is 50 m for a vehicle with a maximum authorised mass of up to 3.5 tonnes or a bus, and 80 m for vehicle combinations or other vehicles. The threshold concerns maximum authorised mass, not current weight. Other requirements, such as the speed-based motorway gap, may also apply.