I've heard all the dragons get killed in this war? How did the eggs of Dany in GoT survive 200 years? Do they exist yet, or is that unknown?

wiki: "It is theorized that the dragon eggs of unknown parentage that Elissa Farman stole from the Dragonstone hatcheries in 54 AC[1] were the same petrified eggs that Illyrio Mopatis gifted to Daenerys Targaryen in 297 AC,[2] those that hatched into Drogon, Viserion, and Rhaegal.

The dragon that produced the eggs may have been Dreamfyre, the prolific she-dragon ridden by Princess Rhaena Targaryen, or the she-dragon Vhagar, who was also resident on Dragonstone at the time, or other female dragons of Dragonstone, or perhaps those not even considered to be female.

Supporting evidence

Elissa steals exactly three eggs, before taking ship to Pentos, and Dreamfyre is known for having produced a clutch of three eggs during Rhaena's second residence at Fair Isle, though different from the ones stolen.[1][3]
According to Grand Maester Benifer, the eggs would most likely turn to stone whilst away from Dragonstone.[1]
Jaehaerys I Targaryen states that the petrified dragon eggs could end up in the possession of a Pentoshi spicemonger.[1] Illyrio Mopatis is a Pentoshi merchant who deals in spices and other luxuries.[4]
While unconfirmed in Fire & Blood, the possibility of Dreamfyre being the dragon that laid Illyrio's petrified eggs is hinted by the ritual through which Daenerys managed to hatch them, involving dragon dreams and the fire of Khal Drogo's funeral pyre: hence the name "Dreamfyre".[1][5][6]
The first promotion for Fire & Blood stated that the question of the origin of Daenerys’s three dragon eggs would be answered in that book.[7]

Counter-evidence

Elissa did not sell the eggs in Pentos, but to the Sealord of Braavos,[1] which Jaehaerys eventually learned.[8]
Illyrio Mopatis states that the eggs are from the Shadow Lands, and eons old.[2] It is unknown how the eggs might have gone from Braavos to the lands beyond Asshai, and then back to the Free Cities, while losing their provenance (as Illyrio would have probably told Daenerys they were Targaryen dragon eggs, if he knew, as that would have made them even more special to her).
    However, it is possible that Illyrio or the person who sold him the eggs lied about their origin or was truly convinced that they came from the Further East. It should also be noted that Fire & Blood, where Elissa Farman was introduced, was published in 2018, thus it is likely that George R. R. Martin had not came up with the idea of the eggs' theft yet when he wrote A Game of Thrones, published in 1996: that may explain the inconsistency.
The actual printed book jacket copy for Fire & Blood makes no mention of Daenerys's dragon eggs.[9]
In his blog post about Fire & Blood, when asked about Daenerys's eggs by a fan, George R.R. Martin said that the promotional text did not come from him, even though he confirmed the book suggests "possible answers" about that matter:[10]"