Rav Pappa said: this is what it means:

At a time when there is peace—they shall be for joy and gladness;

if there is persecution—fasting;

if there is neither persecution nor peace—if they wish, they fast; if they wish, they do not fast” (Rosh Hashanah 18b).
Is it possible to say that there is already peace? Or perhaps the definition of peace is that there are no wars at all?

It seems to me very difficult to say that there is already peace, and certainly not that the One whose name is Peace has already caused His name to dwell here (that is, that the Temple has been built).

Hello Rabbi 🙂 I came back to this issue after a break of several years… in light of the upcoming fast:
Regarding the statement “if they wish, they fast,” etc. …

Who are “they wish”? The collective? The Sanhedrin? And what do we do today when there is no authorized body? Who decides whether they wish to fast or not?

In the Tur, Orach Chayim, section 550, it appears that the matter depends on the will of the majority of the Jewish people; that also seems to be the view of his father, the Rosh, in Rosh Hashanah there. And Nachmanides wrote likewise in the book Torat HaAdam. There are halakhic decisors from whom it emerges that it depends on the will of the different communities (and the Ritva wrote: “If the religious court wishes—they fast,” and perhaps that is what he meant). But in Maimonides’ Commentary on the Mishnah, it sounds like the matter depends on the will of each individual.
The halakhic decisors wrote (the Tur there) that in our times people chose and adopted the practice of fasting, and therefore it is forbidden to breach the fence; all the more so in generations in which there is persecution, when there is an obligation by words of tradition to fast.
It seems that this depends on the will of the Jewish people as a whole, unless there is a distinct community with a different custom. It is not reasonable that it depends on a private individual. Today, the custom is to fast.