Wikipedia has a lengthy discussion with a number of sources in the footnotes.
Regarding the legend that they were found alive in the cave centuries later, that legend seems to have been popularized during the Middle Ages. What seems to have actually happened is that the seven were martyred, either by being walled up in the cave while alive, or tortured to death and having their remains interred in the sealed cave, and centuries later their relics (i.e. the remains of their dead bodies) were found in the cave. So they were commemorated as martyrs.
Regarding their feast being “suppressed” by the Church, I see where you probably got that info (a Britannica article) but I don’t think their feast was ever universal. It seems to have been celebrated as a local feast only in parts of Europe, such as German-speaking countries where “Seven Sleepers Day” was regarded as sort of a Groundhog Day equivalent for weather prediction. I use some old Missals in English from the 1700s and 1800s in my research, and this feast isn’t in them. The Seven Sleepers also weren’t removed from the calendar during the 1969 “demotion” of saints whose existence was considered questionable (see Mysterii paschalis (1969), Pope Paul VI), and it seems clear that seven martyrs actually did exist with their remains having been moved to Marseilles for veneration. So they would seem to be among the many early Christian martyrs who had a traditional, non-universal feast day that simply faded away and ceased to be celebrated over time.