The most detailed work on this period is The Sons of Bayezid: Empire Building and Representation in the Ottoman Civil War of 1402-1413 (2007) by Dimitris J. Kastritsis, though it's published by Brill, which means it's insanely expensive - get it through a library if you're interested.

Anyway, to answer this question we have to begin with the situation created by Timur after his victory in 1402. After he captured Sultan Bayezid, Timur set about looting Ottoman territories in Anatolia and setting up puppet rulers. Sultan Bayezid had recently conquered a whole host of other Turkish principalities and Timur started by re-establishing these, as their administrative structures were simple to re-establish under the control of members of their old dynasties. In territories that had been under Ottoman rule for much longer, however, this didn't happen. There were no old dynasts to put in charge, and so these territories were left in Ottoman hands, with the sons of Bayezid expected to act as vassals of Timur.

So there's the first part of the answer: Ottoman territories in Europe were entirely untouched, and long-held Ottoman territories in Anatolia, while looted, were left under their control. For the most part, the only territory that was lost was that which had been recently gained under Sultan Bayezid. Timur left Anatolia in 1403 and went home, satisfied with the nominal acceptance of his rule and not interested in trying to establish firm control. The foundations of Ottoman rule were not really shaken as a result of what had occurred.

The territories that remained were divided among Bayezid's various sons. This situation could have been a great opportunity for Christian states in the Balkans to unite against the Ottomans, but they were themselves divided. Pro-Ottoman groups existed in states like Serbia and the Byzantine Empire, inspired either by internal factionalism or by fear of a potential Latin Christian takeover, while Latin states like Venice and Genoa were more interested in securing beneficial commercial treaties than fighting the Ottomans. These groups aligned themselves with whichever Ottoman prince seemed most prepared to support their own interests, rather than seeking to fight against the Ottomans in general. This approach did win them some concessions: the Byzantines, for example, were able to recover a small amount of territory during the course of the civil war. In retrospect, though, it's clear that the Balkan states didn't use this opportunity to the extent that they could have.

Lastly, the civil war itself was not nearly as destructive as its length would imply. Territory changed hands rapidly and without resistance according to whichever prince seemed to be on the rise, and it was bisected by a long period (1404-10) in which there was little to no fighting at all. A simplified chronology would go as follows:

• 1402-3: The sons of Bayezid establish themselves in various parts of the empire, Süleyman in Europe, İsa in western Anatolia, Mehmed in eastern Anatolia, with Musa in his court. Mehmed defeats İsa in battle, and now rules all Ottoman territories Anatolia.
• 1404: Süleyman crosses the Sea of Marmara and conquers western Anatolia.
• 1404-1410: Stalemate between Süleyman in Europe and western Anatolia, and Mehmed in eastern Anatolia.
• 1410-1: Having left Mehmed's court at some earlier point, Musa gathers allies and invades Süleyman's European territories, killing him.
• 1412-3: Mehmed makes two attempts to invade Europe, the second is successful and ends in Musa's death and the empire's reunification.

The civil war was highly damaging for the Ottoman dynasty's image, and it would go on to struggle with the question of how to properly handle succession for a long time. First came Mehmed II's (r. 1451-81) so-called "law of fratricide" that required newly enthroned rulers to execute all of their brothers in the name of stability, then after 1603 there was another shift toward seniority, with princes no longer permitted to establish households in the provinces, away from the eyes of the palace. But what the civil war of 1402-13 didn't do was materially drain the resources of the Ottoman state - it was a drawn out conflict for sure, but not an exceptionally bloody one. The thing to keep in mind is that the various groups involved had little to gain from an all-out conflict. Most were just trying to figure out which of the several princes was the correct one to swear allegiance to, and thus would be more likely to switch sides or surrender when faced with the rising fortunes of another prince rather than try to resist. The princes themselves, of course, had a lot more to lose.