And the "documents shown below clearly that it did" means what to you
Document 1
The first concrete assurances by Western leaders on NATO began on January 31, 1990, when West German Foreign Minister Hans-Dietrich Genscher opened the bidding with a major public speech at Tutzing, in Bavaria, on German unification. The U.S. Embassy in Bonn (see Document 1) informed Washington that Genscher made clear “that the changes in Eastern Europe and the German unification process must not lead to an ‘impairment of Soviet security interests.’ Therefore, NATO should rule out an ‘expansion of its territory towards the east, i.e. moving it closer to the Soviet borders.'” The Bonn cable also noted Genscher’s proposal to leave the East German territory out of NATO military structures even in a unified Germany in NATO.[3]
Second part which you failed to read even though you copied and highlighted it "German Unification TREATY of 1990"
The “Tutzing formula” immediately became the center of a flurry of important diplomatic discussions over the next 10 days in 1990, leading to the crucial February 10, 1990, meeting in Moscow between Kohl and Gorbachev when the West German leader achieved Soviet assent in principle to German unification in NATO, as long as NATO did not expand to the east. The Soviets would need much more time to work with their domestic opinion (and financial aid from the West Germans) before formally signing the deal in September 1990.
Also
The conversations before Kohl’s assurance involved explicit discussion of NATO expansion, the Central and East European countries, and how to convince the Soviets to accept unification. For example, on February 6, 1990, when Genscher met with British Foreign Minister Douglas Hurd, the British record showed Genscher saying, “The Russians must have some assurance that if, for example, the Polish Government left the Warsaw Pact one day, they would not join NATO the next.” (See Document 2)
Not once, but three times, Baker tried out the “not one inch eastward” formula with Gorbachev in the February 9, 1990, meeting. He agreed with Gorbachev’s statement in response to the assurances that “NATO expansion is unacceptable.” Baker assured Gorbachev that “neither the President nor I intend to extract any unilateral advantages from the processes that are taking place,” and that the Americans understood that “not only for the Soviet Union but for other European countries as well it is important to have guarantees that if the United States keeps its presence in Germany within the framework of NATO, not an inch of NATO’s present military jurisdiction will spread in an eastern direction.” (See Document 6)