Scrooge McDuck in Duck Tales 2017 is probably not immortal like Zeus, Storkules, or Selene, but has greatly extended his life by at least one supernatural method. Since Webby is only 10 or 12 years old, Scrooge who is about 10 to 15 times her age may seem like an immortal to her.
I don't believe that a totally official death date of 1967 or any other year is given for Scrooge McDuck in the comic books, and thus writers of other comics might possibly depict him as alive in a fictional date after 1967. And for all I know there could be some comic books where Scrooge is active in a fictional year after 1967.
Scrooge's age is discussed in the Wikipedia article on him:
According to Carl Barks' 1955 one-pager "Watt an Occasion" (Uncle Scrooge #12), Scrooge is 75 years of age. According to Don Rosa, Scrooge was born in Scotland in 1867, and earned his Number One Dime (or First Coin) exactly ten years later. The DuckTales episodes (and many European comics) show a Scrooge who hailed from Scotland in the 19th century, yet was clearly familiar with all the technology and amenities of the 1980s. Despite this extremely advanced age, Scrooge does not appear to be on the verge of dotage, and is vigorous enough to keep up with his nephews in adventures. With rare exceptions, there appears to be no sign of him slowing down.
Barks responded to some fan letters asking about Scrooge's Adamic age, that in the story "That's No Fable!", when Scrooge drank water from a Fountain of Youth for several days, rather than making him young again (bodily contact with the water was required for that), ingesting the water rejuvenated his body and cured him of his rheumatia, which arguably allowed Scrooge to live beyond his expected years with no sign of slowdown or senility. Don Rosa's solution to the issue of Scrooge's age is that he set all of his stories in the 1950s or earlier, which was when he himself discovered and reveled in Barks' stories as a kid, and in his unofficial timelines, he had Scrooge die in 1967, at the age of 100 years.
In the 15th episode of the 2017 DuckTales reboot, "The Golden Lagoon of White Agony Plains!", it is revealed that Scrooge was "stuck in a timeless demon dimension" called Demogorgana for an unknown amount of time, which is used to explain his young look. In the 21st episode, "The Other Bin of Scrooge McDuck!", Webby Vanderquack's research on Scrooge reveals that he was born in 1867, as previously established by Rosa. This would make Scrooge 153 years old as of 2020.
Scrooge is depicted as extremely old in the Duck Tales 2017 television series, which clearly takes place during the 21st century.
In "the Secrets(s) of Castle McDuck!" Aug. 4, 2018, a paper is found with the date April 15, 20__, the last 2 digits obscured from the view of the audience. That was the week that Huey, Dewey, and Louie were born, but since Della was at Castle McDuck then, and she was lost in space before they hatched, they must have hatched sometime between April 15 and April 22 of that year.
Since Della was lost "ten years" before the first season, I think it is more likely the boys were 9 in "the Secrets(s) of Castle McDuck!" and turned 10 a few day later, instead of being 10 and turning 11. And Castle McDuck is only reachable for a short time every five years, putting "the Secrets(s) of Castle McDuck!" 10 years after Della was lost in space.
So Huey, Dewey, and Louie were born sometime during the period of 2000 to 2099, and the first season of Duck Tales 2017 hapepns sometime during the period of 2009/10 to 2108/09.
According to this list of the proper viewing order and fictional date order:
"The Impossible Summitt of Mount Neverrest!" happens before "McMystery at McDuck McManor!" which happens before "the Secrets(s) of Castle McDuck!". Since "The Impossible Summitt of Mount Neverrest!" happens during Christmas time, and "the Secrets(s) of Castle McDuck!" happens in April of the next year, "McMystery at McDuck McManor!", where Scrooge has a birthday party, happens in between them in the early part of the next year.
In "The Other Bin of Scrooge McDuck!", which happens after "the Secrets(s) of Castle McDuck!", Webby reads from a book (titled The Life and Times of Scrooge McDuck) that Scrooge was born in 1867.
If "McMystery at McDuck McManor!" happens sometime during the period of 2010 to 2109, Scrooge's birthday in it should be his 143rd to his 242nd birthday.
"The First Adventure!", November 16, 2020, opens in the 1960s, where Mrs. Beakley, Bradford Buzzard, and Black Heron are already adults - Buzzard and Heron decide to found F.O.W.L. The rest of the episode happens decades later when Scrooge has to take care of young Donald and Della and they go on their first adventure together. Since Mrs. Beakley, Bradford Buzzard, and Black Heron are still rather agile in the 3rd season, for the sake of plausibility the episodes of Duck Tales 2017 shouldn't happen any later than the years they are broadcast in, and preferably earlier.
So Scrooge should turn 143 to 150 in "McMystery at McDuck McManor!".
In "the Golden Lagoon of White Agony Plains!", June 23, 2018, Scrooge returns to the Yukon and meets his old rival and love interest Goldie O'Gilt where they had tangled over a hundred years earlier. They each explain - truthfully or otherwise - how they managed to still be alive. I believe that Scrooge's explanation was that he spent a lot of time in a timeless demon dimension.
And possibly Scrooge also spent several decades at Castle McDuck, where he would not have aged. Maybe Scrooge thought living at Castle McDuck with his disapproving father Fergus was like being trapped in a horrible demon dimension!
I note that in "The First Adventure!" Donald and Della look like they were probably born around 1980 in the Duck Tales 2017 chronology, which means their mother Hortense McDuck should have been over a century old when they were born - unless Hortense and/or Donald and Della spent many decades in Castle McDuck without aging.
Scrooge's and Hortense's sister Matilda shows up a Castle McDuck in "The Fight For Castle McDuck!",November 23, 2020, which implies that other McDucks may have avoiding aging by staying at Castle McDuck and/or by living in a demon dimension.
I discuss the chronology of Duck Tales 2017 in threads like:
So Scrooge is not immortal in Duck Tales 2017 but has greatly extended his life by at least one supernatural method. Since Webby is much younger (I think she is about 11 in "How Santa Stole Christmas"), Scrooge who is about 10 to 15 times her age may seem like an immortal to her. Or she may mean Scrooge is someone with everlasting fame and thus figuratively immortal.