What is the ruling on the action of an Imam who sometimes recites a single verse in the first rak'ah to encourage worshippers to come early and not be late for prayer, and is he considered sinful for that?

The Imam must follow the Sunnah regarding recitation and continue advising those who lag behind. The Sunnah is to lengthen the first rak'ah of the Dhuhr prayer so that people can catch it. If the late arrival of the congregants is due to their reliance on hearing the Imam's recitation through the microphone, it is preferable to turn it off.

If the congregants are late without an excuse or are negligent in catching the beginning of the prayer, relying on the Imam's lengthening, and are not deterred by advice, then there is no harm if the Imam sometimes shortens his recitation to encourage them to come early and catch the prayer from its beginning. This measure is restricted to the strong presumption that it will benefit them and prompt them to hasten, not to provoke their displeasure or cause them to miss the beginning of the prayer. If they do not benefit from this, then he should pray as usual and continue advising them.