The ending of The Rings of Power perplexed viewers for all sort of reasons, including narrative choices associated with characters not original to the Amazon tv series like Celeborn and Isildur, whose fate is left very ambiguous. In the improbable case that anyone new to the LotR franchise began with The Rings of Power, they might wonder if Isildur died.
Did Isildur Die in The Rings of Power?
The Rings of Power leaves Isildur's fate ambiguous after the battle in the Southlands, with his father and other fellow Numenorians going home without him and presuming him lost. However, even surface familiarity with the LotR canon confirms that Isildur cannot be dead.
Isildur might not be part of the narrative present in The Lord of the Rings but he's a very important character and often mentioned as one of the people that were corrupted by the One Ring.
In Tolkien's works, after Numenor was drowned, Isildur fled with his father and later become king of Arnor and Gondor.
During the War of the Last Alliance at the Second Age of Middle Earth, Isildur played a key role in the defeat of Sauron by cutting the One Ring off Sauron's finger. However, he was unable to destroy the Ring despite being urged by Elrond to do so. Instead, Isildur kept the Ring for himself.
How Did Isildur Die?
Isildur got attacked by Orcs after the events above, at which point the Ring got lost in the rover Anduin. Tolkien provides accounts of Isildur's death in both The Silmarillion and Unfinished Tales, with more details found in the latter.
Why Is Isildur Presumed Dead in The Rings of Power?
It's hard to tell why the story of The Rings of Power took a turn that causes other characters to presume Isildur there. While it isn't unnatural for them to think so under the circumstances, it feels bizarre that the show creators put them in such a position in the first place.
Even LotR fans who haven't read the books have heard of Isildur and his role in the destruction of Sauron (and non-destruction of the Ring) so it doesn't make sense to create a situation in which Isildur is presumed dead, as it adds no suspense and any sadness (and later relief when Isildur turns out alive) will feel forced since most viewers already know what will happen.
The Rings of Power did change the lore quite a bit, but it's unlikely that they would kill off a character with such a pivotal role at the end of the Second Age, which makes the supposed cliffhanger feel cheap.
Related: The Rings of Power: Why Do Humans Hate the Elves in The Rings of Power?