I think the subquestion here is one of identity - did the average Byzantine citizen identify with the Empire? Nationalism is a newer concept, so I don't know if the standard idea of patriotism applies in the late 14th century.
Would a Byzantine Citizen, circa 1395, have even been aware of how much their empire shrank over the previous two centuries? And how did they become aware?
Ottoman Army claiming victory after victory had a depressing effect on Byzantine citizens (Romaioi). But the largeness of an empire is a different concept. I'm not sure if average citizen could grasp it. With that said, intelligentsia, especially historians were in grief.
Here is what Donald M. Nicol[1] writes:
The last century of the Byzantine Empire was a prelude to the history of the Ottoman Empire that was to take over its provinces and finally its capital in 1453. Decline is dispiriting. No Byzantine historian living in the second half of the fourteenth century felt inspired to narrate the unhappy events of his age. The long and lively tradition of Byzantine historiography ended where Gregoras and Kantakouzenos down their pens about 1360.
Byzantine historiography consisted of heroic characters, narratives resembling epics, passionate writing enriched with dialogues, eulogy/elegy-style dramatization, agenda-pushing... The mesmerizing genre of history-writing that we call Byzantine Historiography had ended in 14th century.
After that (13th century), the sorry state of the rapidly dwindling empire of the Palaiologi hardly favoured epic or even encomiastic treatment of the rulers who presided over one disaster after another. The only exception was the ex-emperor John VI Kantakouzenos who wrote his own apologia for his ultimately catastrophic interventions in imperial politics[2].
[1] Donald M. Nicol, The Last Centuries of Byzantium
[2] Paul Magdalino, Byzantine Historical Writing between 900-1400, The Oxford History of Historical Writing Volume II
To ask a follow up (if that's allowed), how much, if any, hypothetical nationalist feeling would be tied to "Rome" and its legacy rather than specifically Byzantium?
Give or take the definition of citizen.
Was the suggested example a citizen of a sub state of the Empire, or of the heart?
When all roads led to Rome, cui Bono?