Man, this 272 years is just a blink of an eye in our great 7,000 years history ....
In fact, it actually took 365 years. It startedofficially just after the war of Ridaniye in 1517 and ended with the occupation of British empire in 1882.
The Egyptian -Khidivate- you mentioned (my guess) was actually linked to the Ottoman central state in its foreign affairs but it had free will on its domestics. (Just like Algeria)
Mehmet Ali Pasha, the founder leader of the Egyptian Khidivate and former Vilayet-i Mısır governor, also comes from a balkan Turkish family, originally from Konya, according to the Ottoman archives. (This issue is also related to the Ottoman settlement system. As an example, my family migrated to Anatolia after the balkans were lost, but our family records in the Ottoman archives are based on Konya-Karaman. Also modern Turkey's founding leader Atatürk's family had a similar history.)
In the same period, the Egyptian Khidivate Army structure was based on Turkish officers and traditional system. So as you explained here, the situation was not a nation conflict, but a dynasty struggle. (Egypt vilayet's naval ship orders to France and others were blocked from Istanbul, during theirs prefecture of Egypt. With the claim on Syria, the role of this intervention in the leap of the struggle to an international dimension is great which involving the other countries, but these can be discussed in another title and related section.)
Anyway... Despite all this, Turkey's legal rights on Egypt has ended with an international peace agreement in Lausanne.
Article 17 of the Treaty of Lausanne has excatly contain the following statement: "Turkey have been waive on the legal basis from Egypt and Sudan and this new legal status effective from November 5, 1914."
Legal bonds between Turkey and Egypt were end since 1914 according to international laws. And defacto status started with the occupation of British empire. Beyond that, everything is relative historical interpretations.
Even legal status may vary, even if the Egypt and Turkey dragged to geopolitically separate pole, the link between the two nations was never break. Turkish community in Egypt has never been separate from its nation, culturally or politically. (Of course, it is necessary to consider Egypt's history of military coups separately. Arab nationalist policies had negative effects on Egyptian Turks.)
Of course, this cultural affinity and neighborhood relationship could not only be created with the Ottomans.
There is an -our common- history dating back to Tolun Bey, one of the Nine Oghuzes in the 9th century. Tulunids has great importance in terms of Turkish history. It is the first state established by the Turks who accept Islam. And Turks have reached this honor, in Egypt.
(As you know, Oghuz Turks have had great services to Abbasid caliphate. Baghdad has been saved many times, and even Islamization of Anatolia begins with the another Oghuz leader Tuğrul Bey's great efforts which he saved Baghdad from Buveyh's invasion. Just like Tolunids, for centuries, Seljuks and many Turkish other Turkish Atabeys between these two periods saved Baghdad and the entire Levant - Baghdad geography from being burned and destroyed.)
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Frankly, I find the discussion here ridiculous (for both parties) Trying to read dynastic struggles with today's nationalism could be one of the most important mistakes.
We are so intertwined that it is not possible to write another's history without each other. We are only brothers of each other. Do not upset each other. Governments can quarrel today, and meet tomorrow on common interests; do not wear yourself down for daily / temporary political issues.Best regards.