How can one reconcile the description of the Companions as "knights by day, monks by night" with the saying "there is no monasticism in Islam"?

There is no contradiction between the two expressions; for the description of the Companions as "monks by night" is a metaphorical expression indicating the abundance of their worship. As for the forbidden monasticism (rahbaniyya), it refers to abandoning engagement in earning a livelihood and dedicating oneself entirely to worship, or prohibiting what is permissible. The Prophet, peace and blessings be upon him, clarified this when he responded to those who intended to devote themselves fully to worship (tabattul), explaining that he fasts and breaks his fast, prays and sleeps, and marries women, and whoever turns away from his Sunnah is not of him. The phrase "there is no monasticism in Islam" is well-known but is not a hadith. Ibn Hajar explained that it was not narrated with this exact wording, but rather what was narrated conveys that Allah replaced monasticism with the tolerant, upright religion (hanifiyyah).