How did the Prophet ﷺ bring the Quranic Revelation into public?

Is there anything stated in Hadith literature how the Surahs were transferred to public? In particular the longer ones: Were they first written down accoding to the words of the Prophet ﷺ or did he repeat them until others learned them? I know that the Prophet ﷺ used to recite with his scolars behind him. I can imagine that the early surah were memorised in this way as (even though it takes me quite long to learn a short surah, but I am very bad at memorising). However, he even used to recite in silence (e.g. Muslim 4:44 ), so it was possibly not meant to teach during prayer. I wonder in particular whether the longer, less poetic surahs may have been written down in an early stage.