Sorry for being so late! I saw your question a couple of days ago (I get notified by mail about Germany-related questions) but did not have the time to answer it yet. Your OP doesn't have any replies yet and I doubt that some will show up now.
That's probably related to the fact that your question requires relatively rare, well, "niche" knowledge and that it still somewhat borders on our subreddit's 20 years rule. If you are still interested in the topic, I have to say that unfortunately I'm not really versed in this aspect of the German re-unification too, but I will share what limited insight I can possibly give.
Just like the phase-out of the German Democratic Republic was practically more of an admission of new territories to the Federal Republic of Germany than the foundation of a "new" unified German state, the disbandment of the East German Nationale Volksarmee ("National People's Army", commonly abbr. as NVA) was more of a takeover by the West German Bundeswehr than a fusion of two militaries. Only a small amount of NVA personnel was carried over to the Bundeswehr -- the German Wikipedia (sorry for the source but I don't have anything else on this right now) claims that only 3200 of 36,000 NVA officers did serve in the Bundeswehr after 1992. To add to this, retired NVA service members were listed by authorities as "served in foreign militaries" until 2005 and officers are not allowed to bear their rank with the formal addition außer Dienst ("retired") as their Bundeswehr counterparts are able to do.
Those NVA members that were carried over to serve in the Bundeswehr had to observe special training that prepared them for their service in a new military -- a NATO force with different equipment, different rules, and different ethics. This transition was carried out under the command of a new (short-lived) Bundeswehr regional HQ named Bundeswehrkommando Ost (BwKdo Ost). That only few made the transition is also closely tied to the overall reduction of the size of the armed forces of unified Germany that was one of the conditions by the 2+4 negotiations that paved the way for the reunification. During the Cold War the armed forces of West Germany were the backbone of NATO forces in Central Europe with close to half a million soldiers and a large tank force, and on the other side of the fence the GDR had almost 200,000 men at arms with tons of equipment too. Thus, theoretically, a re-unified Germany would instantly become a military juggernaught in the middle of Europe again, which, to no surprise, was in no one's interest. Especially not in the Soviets' as it was agreed upon that re-unified Germany would be part of NATO. Therefore it was stated that the size of Germany's armed forces should not surpass the mark of 375,000 and that there would be no nuclear forces stationed in the territory of the former GDR. That was obviously a significant downsizing for the German militaries, but in a climate of overall peaceful change, disarmament, and the end of the Cold War world order, it was mostly welcomed. Actually, as of now, the Bundeswehr is even smaller than the stipulated size.
So, what happened to all the Warsaw Pact equipment? Well, most of it was apparently sold to other states -- deals of which I don't know much details. Indonesia, Greece, and Turkey were among the clients, most of them already regular buyers of (West) German hardware. But of course not before much of it could be tested by the highly intrigued NATO analysts. After all, the Bundeswehr was the first NATO force to ever get their hands on a huge amount of undamaged Soviet-built military hardware! (Although much of it turned out to be not the first rate stuff that the Soviets preferred to keep for their own forces.) For example, West German Luftwaffe pilots were able to test out a number of East German MiG-29, which at the time was the preeminent fighter aircraft of Soviet origin. These were later sold to Poland for their airforce which regularly uses MiG-29. I'm no military expert, but I can guess that the insights won by this were tremendous.
Here are some links regarding the service of East German MiG-29 in NATO: 1 2
Hope this helps a bit!
I can't speak for much more than one small aspect of this, but the ability to thoroughly evaluate the GDR Mig-29 and the Vympel R-73 (NATO called it the AA-11 Archer) missile it carried had a profound impact on certain aspects of the air to air combat philosophy and research efforts of the Luftewaffe.
To try and summarize, the Mig-29 is a short ranged twin engine fighter, with very good low speed turning capabilities, the missile it carried is incredibly maneuverable, with a very high off-boresight capability aided by a helmet mounted sight. This means the pilot can simply look at a target to engage it with a missile, instead of having to turn the entire plane around to face the target.
In a close ranged engagement (dogfight) this proved to be an enormous advantage.
Even against the latest Block 50 F-16s the MiG-29 is virtually invulnerable in the close-in scenario. On one occasion I remember the F-16s did score some kills eventually, but only after taking 18 ‘Archers’. We didn’t operate kill removal (forcing ‘killed’ aircraft to leave the fight) since they’d have got no training value, we killed them too quickly. (Just as we might seldom have got close-in if they used their AMRAAMs BVR!) They couldn’t believe it at the debrief, they got up and left the room!
(Note that the Luftewaffe was not operating the modern F-16, it had the venerable and somewhat inferior F-4 phantom series which it was in the process of modernising with the KWS program)
Leading up this FRG had been working in tandem with the UK on the development of the ASRAAM (Advanced Short Ranged Air to Air Missile) to replace the AIM-9 sidewinder variants used by both nations (and NATO) which had a longer range than the other short ranged missiles used in the day. Their experiences with the R-73 had such an impact on their conceptions of SRAAM design philosophy that Germany withdrew from the ASRAAM program and instead developed the IRIS-T missile which had a much higher emphasis on maneuverability.
Now the Mig-29 in use by the GDR at the time was not a first rate model.
It is rather important to keep in mind that Germany operates some of the earliest models of MiG-29 - not even the baseline Fulcrum-A but downgraded versions of the MiG-29s employed by Soviet air forces.
And it had some serious drawbacks in other performance characteristics, such as the radar and Beyond Visual Range combat performance.
But its capabilities in a "knife fight" left a pretty big impression after they were revealed.
http://www.16va.be/mig-29_experience.htm
from Jane's At the Controls: MiG-29, by Jon Lake
This post probably violates the rules, but, some might find it interesting from a personal viewpoint. I was a fairly senior staff officer at the 7th Army Training Command in Grafenwoher, FRG, 91-94. I very clearly remember watching a battalion of T72s drive from the railhead to the range. Quite a shock to me as I had spent my company grade years preparing to fight these guys, now they are driving right in front of me, going to train on my facility. Found out later they were an Armored unit of the old GDR that had been incorporated into the FRG army. No idea how long this lasted