Until the 1990s, both governments claimed to be the legitimate government
for China as a whole. The ROC eventually dropped the claim. How did this
change in ROC policy most likely change relations between the two
governments?

The sovereign legitimacy demanded by the government of the Republic of China, in the name of the continuity of a regime founded in 1911 and heir to the rule of Chang Kai Shek defeated by Mao Zedong and confined to the island since 1949, results in the paradoxical situation of Taipei aligning alongside Beijing in disputes in which Washington, which cultivates neutrality in these border disputes, is the military guarantor of regional security vis-à-vis the People's Republic of China.

The two Chinas after recognizing in 1992 the "status quo" of the real existence of two regimes and governments, but accepting by consensus the existence of a single, indivisible China, accelerated the pace of trade, investments and movement of people, despite they are still far from starting to even discuss a peace treaty. After that the relationship between the two Chinas has worsened a lot, currently the situation is chaotic.

a drastic rise in oil prices ended decades of postwar.