The Basic Law of the Federal Republic was interpreted within the Federal Republic[...]
Have to admit I don't understand much of this.
You are correct in saying that the FRG did not become a successor state post-reunification (rather it is still the same, yet enlarged, entity), and this is because the reunification was done under Article 23 of the Basic Law, rather than under Article 146 which was briefly discussed initially (would imply having a new all-German constitution voted into effect by a unified nation).
For the longest time it wasn't clear how unification under Article 23 would work in practice. In theory it allowed for it.
According to Wikipedia (apologies), the unamended Article 23 of the Basic Law:
"provided other de jure German states, initially not included in the field of application of the Basic Law, with the right to declare their accession (Beitritt) at a later date. Therefore, although the Basic Law was considered provisional, it allowed more parts of Germany to join its field of application."
This was great because it was not coercion (forbidden for all time for Germany's past sins), but rather the free expression/self determination of a sovereign people. At the same time, it also meant that those joining would have to subscribe to all existing FRG laws. But the really important part here, actually, was the part concerning "other de jure states". Where does this list of other de jure states that are eligible for accession come from? Why from the FRG maintaining continuity with the German Reich (not to be confused with Third Reich, included under German Reich). But what ended up happening, in the event, is that the GDR joined in a weird hybrid fashion where it initiated accession under Article 23, but then joined constitutionally through a treaty (Reunification Treaty) that recognized it as a sovereign state. One of the implications of the amended Article 23 under which the GDR joined, was that the previous ties by which FRG constitutional courts timed themselves to the German Reich were void. Why? Because the amended and immediately extinct Article 23, said that no one else could ever join, regardless of them belonging to the German Reich at some point or not. That's all. It does not mean that Germany is not a successor state. German leaders still go around the world apologizing for Nazi crimes and paying the reparations bills, which is de facto all that matters really.
This is all really a juridical debate, that has no bearing on practical German foreign policy which maintains that it is a successor state.