I would like to do change the height of the element properties showing in the Inspector from this
to something like this
You can add an Text Area Attribute to your list of strings, like so:
[TextArea(4, 8)]
[SerializeField] private List<string> strings;
The overloads define the size of the text area. In my example it always shows at leas 4 lines of text, and will add a scrollbar, once you have more than 8 lines of text.
Edit: I notice that it is not accurate how Unity displays the amount of lines in the inspector. But I assume this will still work for you the way you want it.