For my Android phone, there is neither a draft section nor an inbox section for the stock message app. All messages, including those you have gotten, those you have sent, and draft ones, are organized with their recipients.
So, when you open your message app again, in message list you will find that draft message which was maybe named as something like '[draft]the text you have entered'.
Download size < 0.12 MB. But also accurate enough, ad-free & free.
The minimalist app available on Play Store: https://goo.gl/ws42fN
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