How to get text wrap working in any shape but rectangles?
There isn’t even a text context menu available for, say, rounded-corner rectangle.

How to get text wrap working in any shape but rectangles?
There isn’t even a text context menu available for, say, rounded-corner rectangle.

Text wrap behaves different depending on the kind of shape. The setting is in “Text attributes”. In Impress, that is in menu Format > Text box and Shape:
[edit]Revision:
Checked in versions 6.2.8.2 and 6.4.4.2, it is not default, but can be adjusted.
Checked then version 7.0.0.0 - it’s default.
[edit]
According to @anon73440385’s and @LeroyG’s comments: Wrapping also exists on version 6.x, but not as default. Sorry for wrong advice.
Checked in versions 6.2.8.2 and 6.4.4.2, you’re right.
Works for me on Linux openSUSE 15.1 / KDE - Plasma5
Works in Versión: 6.3.6.2 (x86) over Windows 7 Professional.
Rubi,
Double-click on the text, open context menu, Text…, Text tab, activate Word wrap text in shape.
First you must select the text (not the shape).
these options do not show up in libreoffice impress 7.4.7.2
here is what I can see when trying to wrap text (none of these options work)

I see, so The default text boxes do not support wrap text, I should then manually replace them with custom shapes them.
Thanks
Each text box supports wrap text. Only make sure that “Fit width to text” is unchecked.