You’re right about the first part, I just remembered the Neue Ostpolitik marking a significant change.
As to the constitution: While the preamble isn’t its own article, it’s just as much a part of the constitution as every other part.
Here’s what the Bundesverfassungsgericht (German Constitutional Court) ruled:
The German Reich continues to exist and still has legal capacity, but is not itself capable of acting as an overall state due to a lack of organization, in particular due to a lack of institutionalized bodies.[…]
The German Democratic Republic belongs to Germany and cannot be regarded as a foreign country in relation to the Federal Republic of Germany.
No constitutional body of the Federal Republic of Germany may abandon the restoration of state unity as a political goal; all constitutional bodies are obliged to work towards the achievement of this goal in their policies - this includes the demand to keep the claim to reunification alive internally and to persistently defend it externally - and to refrain from doing anything that would thwart reunification.
And while German public broadcast isn’t controlled by the government, it is a good indicator for the political beliefs of the general population and the government.
The situation cannot be appropriately compared to the PRC and ROC, as there are significant differences. What can be compared is that the FRG never recognized the GDR as a state legitimated by international law. Just like the One-China-policy, the FRG had a One-Germany policy in its constitution.