If you set the TextBox as Multiline, then it supports a Lines property: an array of strings, with each string element displayed on a new line:
TextBoxBase.Lines Property (System.Windows.Forms) | Microsoft Docs[
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So all you need to do is find the index of each match start offset in your input, and copy each "section" into a new string in your array.
I'd start with a List as you don't know how many elements there will be, then convert it to an array using ToArray to set the Lines property of the output TextBox.