The Reverse-Flash Knows Oliver Queen's History
Strangely enough, the best evidence that Oliver Queen is still around in the not-too-distant future came from Reverse-Flash. When Flash, Firestorm, and Oliver joined forces to fight the Reverse-Flash in The Flash season 1 episode "Rogue Air," Eobard Thawne taunted Oliver by saying that the history books of his time revealed Green Arrow lived to be 86 years old and that he guessed the books were wrong. Thankfully, the other heroes stopped Thawne before he could make good on his threat toward the Emerald Archer.
Given that information, the date of Oliver's death can be roughly worked out from his date of birth, which was revealed in the Arrow season 1 episode "Damaged." It is here that we first saw the tombstone that was erected in Oliver's memory when he was presumed lost at sea, and his birthday is given as May 16, 1985. Adding 86 to 1985 gives us 2071, thus suggesting that Oliver dies in late 2071 or early 2072. In either case, this still gives him a couple of good decades after 2038 and 2046, barring any drastic changes to the timeline.
Theory: Arrow Is Establishing A New Star City 2046
We know that the future seen in "Star City 2046" can't come about exactly as we saw it. For one thing, the Oliver Queen of 2046 told the Legends that they never returned home from their quest to stop Vandal Savage. Not only did the Legends successfully stop Savage but they have returned to their home time-period multiple times over the past three years, even ignoring their appearances in the crossover events Invasion! and Crisis on Earth-X. Sara Lance is currently sharing an apartment in Washington DC with her girlfriend in 2019 when she isn't time-traveling, and Nate "Steel" Heywood retired from active duty as a Legend to take up a desk job with the Time Bureau.
Another key difference between the current-day Arrowverse and the Star City of 2046 is that there is no way for Oliver's secret identity wasn't revealed until 2031. Oliver already outed himself as Green Arrow in Arrow season 6 finale. Quentin Lance died in the same episode, making it impossible - baring a sudden trip to the Lazarus Pit in the next decade - for him to die again in 2031. Still, there are elements of "Star City 2046" that might yet be utilized in crafting Arrow's future. It's still possible that John Diggle may die a hero's death and that his son, blaming himself for not being as good as his superhero dad, might take up a new name while still trying to honor his legacy. Indeed, given John Diggle's time as the Green Arrow, this may explain why John Diggle Jr. would attempt to "become someone else" two-times over.
Assuming what Reverse-Flash said about the history books of his time is true, and still accurate, baring sudden changes to the Arrowverse timeline in The Flash and Legends of Tomorrow, Oliver should still be alive and well in Star City 2038, even if he's in hiding. It's not impossible to believe that he may be biding his time for a comeback to save his city once more or that he is the mysterious figure sending coded messages to William Clayton. This could be building up to the ultimate Dark Knight Returns tribute, with an elderly Oliver Queen training a new generation of heroes to continue his work in the caves under Star City. That would be perhaps the best ending Arrow could hope for.