It seems weird to find no announcement on Bethesda's behalf. Besides, DLC comes out in only two weeks, how much feedback is Bethesda planning to take in? Very little time, very many bugs.
When is the beta going to end? When the dlc launches or before?
It won't "end". When the DLC comes out everyone that has it will get an update that fixes some bugs. The codes they give out are for the ACTUAL DLC. So everyone that gets in will not pay for it. When it comes out to the public, Beta testers will already have it.