Russia has long regarded itself as the “Third Rome,” although of course the rest of the world doesn’t necessarily agree. This began with the fall of Constantinople and has had some currency among Russians for centuries, although it later was connected more with the Russian secular political situation than with anything religious. However, I think that, in addition to working out its relationship with the Catholic Church, the Russian church is now trying to resolve its relationship with (a) the various factions within it and (b) the MP.
As for this meeting with the Pope, it’s an excellent sign, regardless of the internal dynamics, because the Russians used to be extremely hostile to such a possibility and were much more negative than the Greeks or others.
Livius, Constantinople was elevated above more ancient Churches of Alexandria and Antioch for political reasons, and even (older) Rome itself became the Holy See (rather than Antioch) for the same reason.
There is nothing in the Bible that identifies the city of Rome as the Christian "Mecca." It became that because it was the imperial capital. The proceedings from the Third and Fourth Ecumenical Councils make that very clear.
Moscow has every right to consider itself the Third Rome given that the EP is a virtual prisoner of a Muslim state, a relic of history. The MP, on the other hand, has over 80% of world's 300 million Orthodox in his fold. Even more when one adds other Slavic Orthodox Churches (Serbian, Ukrainian, etc.) which would very likely side with Moscow, politicis notwithstanding, because the laity would.
Any reunion with Orthodox without Moscow would be utterly meaningless; in fact it would be a new round of creating a new "uniate" controversy, drawing perhaps 10% of the current orthodox fold and destroying any chance of reunion for ages to come.
I am confident that any reunion will include the Orthodox Church as a whole, with all its Patriarchs and Metropolitans standing united.
As far as the West is concerned, they must show historical and synodal respect for the seniority of Constantinople, but one must be very careful not to marginalize the vast majority of the Orthodox world, especially if such marginalization is based on not much more than sheer prejudice vis a vis Moscow.