Had it not been that I might overburden the believers—or  my Ummah—I would have commanded them to use the Siwāk (toothstick) at every prayer

The Prophet's compassion towards his Ummah and his fear of making things difficult for them.
In principle, the Prophet's command indicates obligation unless there is evidence that it is voluntary.
The recommendation and merit of using the Siwāk at every prayer.
Ibn Daqīq al-Eid said: The rationale behind the recommendation of using the Siwāk when getting up to pray is that it is a state that brings one closer to Allah, which requires its being a state of perfection and cleanness to highlight the honor of such an act of worship.
The general indication of the Hadīth includes using the Siwāk by the fasting person even after the sun's decline, as in the case of the Zhuhr and ‘Asr prayers.