The summary says it:
Pasted text box ends up in layer that doesn't know it's a text layer.

Steps to reproduce:
1) create a new image, 640x480 will do.
2) create a text with the text tool.
3) copy the text
4) paste
5) switch to the layer dialogue and observe the new floating selection
6) create a new layer from the floating the selection.

Here is the problem. The layer gets the name "Pasted Layer". It doesn't show a "T" on white background. You can move the copied text with the move tool, but when you try to edit the copy with the text tool, it's not recognised as text.

If on the other hand, you rotate the original text using the rotate tool, it's layer also loses the "T", but you can still edit the text later. You get a warning and  lose the rotation, but that's acceptable.

What I find strange is that a pasted text layer does not know that it was pasted from a text layer and should therefore also be a text layer.

I looked through the online manual, and there is very little on copying texts.

So either this is a bug, or an enhancement request or at least a documentation bug.

Sure, you can copy a text by just duplicating the layer, there's no problem.