Disclaimer: In regard to why the Ottomans lost the great Turkish war, we don't have a definitive answer. Nobody has written a modern detailed study of the war.
The traditional explanation would be that the Ottomans did not keep up with European developments in the realm of army drill and in the shift from cavalry to infantry, but current research is pushing back against this. Until recently we've been in the dark with regard to how seventeenth-century Ottoman armies fought, relying basically on European observers. Relying on foreign observations is fraught with danger because the observers often write more from their own biases than any real knowledge of what they're talking about - I could cite an Ottoman observer telling you that Austrian musketeers did not know how to aim. So lately we've tried to rely more on what the actual Ottoman sources have to tell us, and they've given us an image of the Ottoman army as being much more "modern" than we thought. For instance, we know that the Ottomans maintained an infantry/cavalry ratio roughly equivalent to that of the Habsburgs and that they also made use of their cavalry as dragoons. We also have very early proof that they were training their infantry in volley formations.
So the Ottoman army doesn't appear to have been all that "backwards," or at least we can't say that with certainty anymore. We can say that the Ottomans definitely had less experience with battle than the Habsburgs. Large-scale battles were far more common in central European wars than they were for the Ottomans if this is what you refer to. However even here this would only be true for the specific period were talking about and not reflective of the ottomans “falling behind” holistically in terms of military capabilities. Habsburg leadership probably knew how to conduct itself in battle better than that of the Ottomans, and this is part of the explanation for why the Ottomans lost most of the major field battles they fought during the war. Sieges were another matter - there the Ottomans were experts.
The context of the war is extremely important. The Ottomans weren't just fighting the Habsburgs and Imperials; they were also fighting Venice, Poland-Lithuania, and Russia. This meant that the war took place on a huge number of fronts. The Ottomans had to divide their forces to fight in Greece, in Dalmatia, in Hungary, in Podolia, and in Crimea. You mentioned that direct ottoman focus against the Russians was minuscule for most of the war. This is true, but you’re forgetting something important. The Crimean Khans were unable to support Ottoman operations in Hungary for pretty much the entire duration of the war because they were defending their territory against the Russian empire, robbing the main Ottoman field army there of its usual enormous light cavalry support (and consequently its ability to engage in effective reconnaissance and harrassment). For Rhoads Murphey, probably the foremost military historian of this era, the logistical strain of trying to fight on so many fronts is the primary reason for the Ottoman defeat.
To this we can add a few other features: one, the defensive structure of the Ottoman fortress network in Hungary was very hollow. Border fortresses were quite strong, but once the exterior fortress line was breached (the fall of Buda, 1686), the Habsburgs could pour through the gap and conquer basically all of central Hungary. If you look at the timeline of Habsburg conquest, you can clearly see this pattern: the Habsburgs reached the Danube very soon after the fall of Buda, but it took them a long time to actually consolidate that position by conquering all the Ottoman border forts they bypassed. By the end of 1686 the Ottoman-Habsburg frontier basically looked like this. The Ottomans were really not prepared to suddenly have their network breached.
Secondly, the aftermath of the Siege of Vienna was a political nightmare. These critical Habsburg advances were occurring during a time of severe instability in Istanbul. The grand vizier Kara Mustafa Pasha was executed for his decision to attack Vienna without the consent of Mehmed IV*, and this led to an attempt to dismantle the whole Köprülü political apparatus that had dominated the empire's politics for the last thirty years. The empire really needed stable leadership but in this crucial moment, it didn't have it. By 1687 Mehmed IV was overthrown and replaced by Süleyman II, which eventually brought about a Köprülü restoration as well. This provided the stability the Ottomans needed to push the Habsburgs back across the Danube and reconquer Belgrade (helped by the outbreak of the Nine Years' War between France and the Habsburgs), but they couldn't get back into Hungary - all their fortresses there remained cut off and were gradually conquered. The fight shifted to Transylvania and ultimately ended with a stalemate on the Danube. The Ottomans couldn't push back north and the Habsburgs couldn't push south.
*Some historians think that Mehmed IV actually ordered the attack, and just shifted the blame to Kara Mustafa after the failure.
I’m afraid that we don’t comp,Evelyn understand each other. I’m not saying that the Ottomans of that period had been hopelessly behind but they were noticeably lagging in some areas.
While they had been traditionally (and well beyond the scope of the period in question) good in defending fortifications and rather proficient in building the field fortifications even in a process of a battle (meaning that they were equipped with the needed instruments better than their Western counterparts, their ability to maneuver on a battlefield was well below that level. Their battlefield maneuvers, even if the ideas sounded good (infantry with cavalry on the flanks), heavily relied upon a fieriness of the attack but if it failed, they were pretty much lost. While reports of the enemies is not the best source but the Russian descriptions from the conflicts of the XVIII (different authors, different circumstances and time span of almost 100 years) are reasonably consistent: Janissary rushing ahead in a deep mass with an intention to defeat the enemy in hand-to-hand fighting (the remedy found was to have infantry in the squares or columns acting offensively). Their cavalry was brave but I’ll-disciplined and had lighter horses than heavy Western cavalry (which was also better drilled to maintain the formations. Ottoman artillery of that period and most of the XVIII was numerous but not necessarily up to date and the crews were not well trained, which made its efficiency quite low.
As far as the sieges were involved, the Ottoman were experts but their expertise was getting obsolete: the “West” was already in the Vaughan-defined world of the fortifications and sieges and the Ottomans were still digging under the walls.
Now, I got your point about the volleys but, I’m afraid that on its own this means little: Russian streltsy had been taught to fire by the volleys and even adopted a linear tactics before GA but on a battlefield they were quite pathetic unless (surprise, surprise) arranged behind the field fortifications and by the end of the XVII were seriously lagging behind their Western counterparts forcing serious military reforms which in the case of the Ottomans did not happen until XIX.
Now, while during the Great Ottoman War the Ottomans did have a strategic nightmare, practically everything you wrote about the Russian “front” is pretty much wrong (sorry). To start with, there was no Russian empire at that time and military activities were rather sporadic:
there were campaigns of 1687, 1689 and 1695 - 96 with practically no fighting in between. In 1687 and 89 Crimea was involved but not the Tatars and in 1695 - 96 it was other way around with the Ottoman forces involved: 3,656 in 1695 and 4,000 more in 1696. Hardly something worthy to talk about as a factor seriously contributing to the exhaustion.
The exhaustion could be a strategic factor (parallels could be made with the WoSS, Napoleonic Wars, etc.) but it has little to do with a battlefield performance and an argument that the imperial forces had been doing more fighting is interesting but not quite convincing. For fighting the Ottomans the Austrians and imperialists figured out a tactics somewhat different from one routinely used in the European wars. The same goes for the Russian-Ottoman war of Empress Anna: Russians did not fight the wars since the GNW and did not fight the Ottomans since the Prut campaign but they figured out an original tactics which, while being far from optimal, allowed the battlefield victories. Ditto for the first Ottoman War of CII: Russian tactics was distinctively different from one of the 7YW. However, it seems that the opposing Ottomans were still tactically operating along the same lines as at Prut.