One of the things to take into consideration when discussing the activities and the extent of the destruction caused by the so called Sea Peoples is that, as you state, not much is known about them. We know with certainty that they were present in the middle east in the year 1207 BCE, as Pharaoh Mineptah writes about them in an inscription (sadly incomplete) found in in Karnak (modern day Luxor), where he lists the different peoples:

“The unfortunate and fallen chief of Libya… has jumped on the country of the Tehenu with his archers: Shardana, Shekelesh, Eqwesh, Lukka, Teresh, bringing with him the best warriors and from his country…

List of prisoners brought from this Libyan land and the countries that went with it:

Sherden, Shekelesh, Eqwesh from the lands of the sea, who didn’t have prepuce:

• Shekelesh, 222 men, totalling 250 hands

• Teresh, 742 men, totalling 790 hands

• Shardana - [totalling] -

• [Eq]wesh that didn’t have prepuce, murdered, from whom the hands were take, (because) they didn’t have [prepuce]

• Kehek and Libyans, brought as living prisoners, 218 men”

Of the peoples listed above, we know little to nothing. Remains that may indicate the a site of origin of any of them have never been found, though linguistic analysis, as well as the study of their ceramics and other remains gave way to hypothesis; it is theorized that the Shekelesh came from Sicily, and the Shardana came from Sardinia, based on linguistic similarities and on the fact that Rameses III later referred to them as “foreign countries instigating a conspiracy in their islands” and the Shardana were specifically referred to as “Sea People” by the aforementioned; other theries, however, suggest these two peoples originated in the eastern Mediterranean and only moved to Sicily and Sardinia after being defeated by the Egyptians, thus naming the islands after themselves, a theory backed by the knowledge that the Shardana had fought against Egypt prior to the arrival of the “Sea Peoples” and deterred by an inscription by Rameses II where he states that the surviving attackers were forcefully settled in Egypt. Other peoples have been identified with much larger consensus, such as the Denyen, which were identified as the Danaus from Homer’s Iliad, and the Peleset were identified as Philistines. Others have been identified among uncertainty, without much of an existing debate, such s the Eqwesh, who have been identified as the Aqueans; the Lukka, who have been iedntified as belonging to southeastern Turkey; and the Teresh, commonly asociated with the Italian Etruscs.

The Denyen and the Peleset would not be present in the wave of attacks around 1207 BCE, but would be part of a second wave 30 years later, in 1177 BCE, of which we know of thanks to the many inscriptions Rameses III ordered describing their arrival and subsequent defeat at his hands.

“The foreign countries instigated a conspiracy in their islands. They suddenly striked against all lands and dispersed them in combat. No land was able to resist against their weapons, from Jatte, Qode, Karkemish, Arzawa and Alashiya, all isolated [at the same time. Established] a camp near a place in Amurru. They devastated their peoples and their lands was left as the one that never existed. They advanced towards Egypt, with flame ready in anticipation. It was a confederation of the Peleset, Tjekker, Shekelesh, Danuna and Weshesh, the united lands. They put their hand over the lands of the entire circuit of Earth, with their heart safe and confident. “ -Rameses III, inscription in the funerary temple of Medinet Habu

He continues later:

“Of those who reached my frontier, their existence is gone, their hearts and their souls are forever ended. To those that ventured together into the sea, the flame awaited them in the estuaries, and in the coast a wall of spears surrounded them. They were dragged with them, rounded, thrown on the beach, killed and piled, from the first to the last. Their ships and their goods, it was as if they had fallen to the water. I have made their countries refrain from even mentioning Egypt, because when they utter my name in their lands, they burn to death.”

We know more of them, of course, but besides what was written by the Pharaohs Mineptah and Rameses III, it all falls under uncertainty and speculation, as there are very little remains that can be consistently tied to them. So knowing that, it seems mostly impossible to truly know whether Troy fell prey to them or not, though further investigation may provide evidence.

The city of Troy itself was found by Heinrich Schliemann during the XIX century, in the site of Hisarlik, Turkey. Nine cities were found, one on top of another, and thus far, no consensus has been found on which of them belongs to the legendary Troy.

The sixth city, Troy VI, was originally believed to have been destroyed around the year 1250 BCE, though it is now believed that it was a bit earlier, around 1300 BCE. It was clearly a rich city, with objects imported from Mesopotamia, Egypt and Cyprus being found; and it was situated right between the Hittites and the Mycenaean. Dörpfeld posited that the city was taken by the Mycenaean and burned to the ground, inspiring the posterior legends. Blegen, however, believed the city had been destroyed by an earthquake, not by humans, an argument backed by the presence of displaced walls and sunken towers, and by the absence of arrows, swords or other military-related remains within the ruins of the city. He also believed the more likely candidate to being the Troy of Homer was Troy VIIa, whose destruction is currently dated at 1180 BCE, only three years before the arrival of the “Sea Peoples” in Egypt, which would unlock its destruction at their hands as a possibility.

Now, having briefly (perhaps too briefly, I’d be glad to expand if necessary) summarized our current knowledge of the Sea Peoples and of of the city of Troy, let us dive into the two main theories regarding the historical background for Homer’s Iliad.

The first theory refers to a rebellion within Hittite territory during the reign of Thudaliya I/II (it is unclear which of the two kings governed at the time). At the time, Thudaliya I/II was returning from a military campaign in western Anatolia, when a league of rebellious states was formed under the name of Assuwa in north-western Anatolia. The Hittite army was then supposedly rerouted towards Assuwa, where the rebellion was suffocated. Thudaliya would write: “Ten thousand soldiers from Assuwa, six hundred chariots and their horses and the subdued population, their oxes, their sheep and the fruits of the land were brought to Hattusa as prisoners. “

Among the prisoners were the king of Atussa and his son, Kukkuli, along with other royality. Kukkuli was made the new king of Assuwa as a vassal to the hittite kingdom, thoug he would later spring a second revolt, that would again be suffocated. This time, the kind was executed and the league of Assuwa destroyed. All that was left was its name, from which Asia was derived.

Hittite tablets name the 22 states associated with the league, and though none of them can be identified, two names come to attention: Wilusiya and Taruisa, which are believed to be the posteriorly named Ilium and the Troad, that is to say, Troy and its surroundings.

One of the main pieces of evidence that would support this rebellion springing the legends of Troy is a sword found in Hattusa, the Hittite capital, bearing an inscription from Tudhaliya I/II referring to Assuwa. The sword’s design is clearly of Mycenaean origin, which begs the question, why was a Mycenaean weapon being used in Assuwa’s rebellion and how did end in Hittite hands? Was it part of the loot? If so, does that imply that the Mycenaean fought with Assuwa?

Unfortunately, those are questions to which we have no answer.

The second theory, speaks of a rebellious Hittite subject named Piyamaradu, who attempted to destabilize the region in a series of conflicts during the reign of Muwattalli II, one of which ended in the defeat of a local vassal king named Manapa-Tarhunta. Thanks to a letter from Hattusili III to an unidentified Mycenaean king, branded the Tawagalawa letter, we know that these rebellious activities continued under the reign of the aforementioned, as the letter details how Piyamaradu assaulted the lands of western Anatolia and apparently received asylum in Mycenae. The same letter talks of Tawagalawa, supposedly the brother of the Mycenaean king, who was currently mustering men hostile to the Hittite kingdom in western Anatolia, despite having “ridden in the chariot alongside the king’s personal auriga”, which indicates Hittite-Mycenaean relations had been much better in the past and were now deteriorated. The same letter also references a dispute between the two countries for a region named Wilusiya, just as the region that rebelled under the Assuwan league.

With this, the theory states that the war of Troy would have truly been a conflict between these tow powerful nations for the lands of Troy.

In conclusion, very little is known about the "Sea Peoples" and very little is known about the city of Troy, but most modern day historians, at least those who investigate in the Bronze age, believe the inspiration for the Trojan War to have come from either the rebellion of Assuwa or the much posterior conflict between the Hittite kingdom and Mycean.