By the point in time Osman came to power, Byzantium is a spent force and it's only a matter of time before they're destroyed.
Honestly, I disagree. Yes, the Empire was in a bad way in the closing years of the 13th century (very bad in fact), however, given enough breathing space, which the lack of the Ottomans would offer, the Empire could enact some necessary reforms and recover something of their old strength.
Heck, Andronikos III would go on to prove that there was at least some gas left in the tank to glean some victories during his reign and that was with the Ottomans at the gates in Anatolia. Heck, he nearly reunified Mainland Greece before his death. Had he lived longer, which he could have (he only died at 44) he could've done more to secure Greece and avoid leaving the Empire in the hands of a child who's regency was fought over, wrecking the Empire in the process.
Without the Ottomans there's a pretty good chance the Empire would retain some of their Anatolian holdings for at least a bit longer than OTL, giving them the opportunity to accomplish something. Is it guaranteed? Heck no! But it's not zero. And the best part? Over the course of the 14th and 15th centuries OTL the general trend was toward a general warming of relations with the West and there's no sign that the PoD in the OP would change that general trend, so more attempts at a Latin take over of Constantinople are going to be increasingly unlikely moving forward, so this means there's more of a chance that the Empire would be far less distracted by the West and could focus their efforts on Anatolia.
Also, for those pushing the notion that another Turkish dynasty would be able to be able to recreate the Ottoman's success in the Balkans (even a little bit), remember, the Ottoman conquest of the Balkans was predicated on an Earthquake in 1354 and being in a position to take advantage of it while the Empire was in a state to be taken advantage of. I think that's rather unlikely to happen.
Also, a Turkish state that couldn't take out the weakened Bulgarians and Serbians and the weakling Greek Statelets probably isn't taking Constantinople, which even the Ottomans found difficult to take in 1453.
Again, is the Empire guaranteed to have a resurgence without the Ottomans around? No. But are they guaranteed to fall like OTL, just to a different Turkish dynasty? Heck no! The 14th century was seriously bad for the Empire, but it required specific events to take place that if they didn't, the Empire would probably limp through the 14th century, seriously weakened with the loss of Anatolia, but still existent and able to affect its own fate.