Well there's two sides to that. The descendants of Turkic peoples, (like the Azeris) who speak Turkic languages, and non-Turkic peoples who adopted Turkic languages under the rule of Turks.

On both counts, there were historically (and in some cases down to the present) plenty of places other than the ones you mentioned where people were speaking Turkish.

So for instance, there are actually way more Azeris in Iran than there are in Azerbaijan. Or you have the Turkmen of Iraq and Syria.

You also should bear in mind the huge population transfers (i.e. quite often ethnic cleansing) that took place as the Ottoman empire lost its European territories. So hundreds of thousands if not millions of Turks in the Balkan territories (including Greece) would become sort of refugees within the boundaries of modern Turkey and vice versa, leaving a Turkey that was free of Greeks and a Greece that was free of Turks.

In the second category, bi-lingualism in Ottoman Turkish was common among the Arab elites of the Ottoman empire. But until the late 19th/early 20th century, the Ottomans were generally content to let local notables and run the show. There was no empire-wide education system or policy. And there was certainly no effort to "convert" Arabs into Turkish speakers. In many instances it was quite the opposite. In Mameluke ruled Egypt, for example, the cultural distinctions between Turkified Mamelukes and Arab Egyptians was strictly maintained and intentionally so.

That changed in the Ottoman empire centralization reforms and with Turkification policies, accelerated under the Young Turks. But those policies were short lived as the empire was broken up shortly thereafter as a consequence of WWI.