After several attempts to do so, I finally won a game through Diplomacy.
The earlier attempts were helpful in learning what to do and not to do, as well as what the AI civs will do to prevent you from winning once you reach 8 out of the 10 Diplomatic Points needed for a Diplomatic Victory.
Interestingly enough, my success was with the Inca led by Pachacuti. I had thought Canada with Wilfrid Laurier, or France with Eleanor of Aquitaine would be the best new civs for achieving a Diplomacy victory, but as I got deeper into the game, I decided that the Inca are well suited for this type of victory pursuit.
It was a fun game, maybe one of the most enjoyable in the series of playing each of the new civs in Gathering Storm for the first time. Avoiding wars, achieving and keeping five alliances, and focusing on diplomatic favor provided a somewhat unique approach for me, but it paid off.
I was attacked fairly early in the game, lost a city, then regained it before settling the war; that turned out to be the only war of the game for me – a defensive war, so not a problem from the diplomacy point of view.
I went into the game knowing I would most likely need to build the Statue of Liberty wonder, because it provides 1 Diplomatic Point upon completion, and Diplomatic Points are difficult to earn. Even though I had only one port city, I was able to do so.
Another important source for those points is Aid Requests from other civs after they have experienced a natural disaster of some sort. In my previous games, I had the disaster intensity set at the default of 2. In those games, I had few opportunities to win the points through Aid Requests because there were so few serious disasters and the AI civs did not request any aid. This time I set the disaster intensity to the maximum of 4. It made a significant difference in the number of opportunities and as a result, I was able to win the game on turn 389 without relying only on the late-game options.
There are two late-game ways to earn guaranteed Diplomatic Points – researching the Seastead tech, and discovering the Global Warming Mitigation civic. I did research the Seastead tech, which gave me an important point – my ninth. The final and winning point in this game came as a result of winning an Aid Request just a few turns before I would have completed discovery of the civic.
One other way to earn Diplomatic Points is through Climate Accords in the World Congress, but I was never offered that option in this game.
Mid-to-later game options for essentially buying Diplomatic Points using Diplomatic Favor are presented as World Congress opportunities. Each time it comes up as a choice, 2 Diplomatic Points are at stake. I was able to win these points three times using a large amount of Diplomatic Favor. The first time was only by one vote, but the other two were not close. If another opportunity had come up after I already had 8 points, all the AI civs would have ganged up on me and voted for me to lose 1 point. That happened to me in another game, putting me too far away to win via Diplomacy and I had to settle for my backup option in that game, Culture.
In the Inca game, I was working on Science as my backup win option if Diplomacy failed again, but it was not necessary this time.
I had so much fun with this game, I think I will be choosing to play to win via Diplomacy regularly.