Germany can probably drag in people from poorer EU members. That'd probably be more popular in Germany than immigration from outside the EU, but doing that transfers German demographic problems to those states when they already have their own demographic problems. If it's a big problem for Germany, it's gonna be an even bigger problem for Bulgaria to deal with on top of existing Bulgarian problems.

With EU total fertility rates as low as they are, the EU is very probably gonna have to accept a considerable chunk of immigration from outside the EU if it intends to maintain its position. Can choose the source to some degree, but it's gotta happen one way or another.