Like so many, I spent countless hours of my childhood playing Civ 1 and 2 as a kid. These were single player experiences that I would play out over several days.
Much later in life, I remember there was a competing game that came out "Civilization: Call to Power" from Activision. It wasn't perfect, but it was some of the most fun I had. You see, that game had support for a type of play called "Play by Email" (PBEM). You could hang out on the Apolyton forums (https://apolyton.net/forum) and co-ordinate a PBEM game with other civ players.
Each player would play their turn, mail it on to the next player, and post an update on the forum. Posts would often be role play .. often with diplomatic messages, declarations of war, expressing outrage, or overtures for peace, or just listings of grievances or demands. People would email each other directly to scheme or perform diplomacy, form secret (or open) alliances and non aggression pacts.
If a player went inactive for too long, we'd get a new player to join the game and take over the helm for their civilization. These games would go on for many months start to finish. Players could be engaged in multiple such games at the same time.
I don't know if the new Civilization games offer this type of gameplay (I do not think they do), but I would love this type of game structure.