It's not that the labels cant be moved, just that the AI forces me to put them on a grid of its own choosing so it jumps about randomly instead of moving to where I drag it.
By default, yEd uses "SmartFree" label placement for nodes and edges. There is no grid for "SmartFree". Actually, there is no grid for any other label placement option either. Maybe you mean SmartFree's snap lines?
Koalabi has actually answered the question: this is as-designed and you cant change the behaviour, only fix it manually and individually for each label.
What is "as-designed"? And which behavior cannot be changed? And how is fixing it for each label not changing? That sentence makes no sense at all. Anyways, it is possible to change the placement option for all node labels at once and for all edge labels at once. Moreover, it is also possible to have all labels placed automatically.
Also your instructions for uploading files must be out of date. This page does not have any icons for link etc.
No, these instructions are not out-of-date. They are spot on. However, they apply to posting a new question or answering a question (as mentioned in the very first sentence), they do not apply to commenting!