Honestly, a lot of people just shout 'AO3!' and call it a day, but you're asking about a specific crossover blend that needs a sharper lens. Archive of Our Own is indeed the powerhouse, but for this mashup, tagging is everything. You'll want to search the 'Harry Potter' and 'Star Wars' crossover category and then filter for 'Immortality' as a tag. Don't skip checking the bookmarks of authors who write that niche well—their bookmarked stories are often hidden gold. I've found some of the best stuff, like a series where a Horcrux-creation-gone-wrong sends a fragment of Voldemort's soul into the young Anakin Skywalker, not by browsing the main tags but by following those bookmark trails. Wattpad has some, but the quality is wildly inconsistent; it's more of a dig-through-piles-of-coal-for-a-diamond situation. I'd steer clear of random forum sites unless you enjoy malware pop-ups more than reading.
There's also a trick on FanFiction.net: their crossover section can be navigated by selecting both 'Harry Potter' and 'Star Wars' as the source materials. It's an older archive, so the prose style tends to be from a different era of fanwriting—more exposition-heavy, sometimes. The immortality angle might be tagged as 'Immortal Harry' or 'Immortal Character' in the summary. I still revisit one from there where an immortal Harry, having lived through countless earth cycles, is discovered as a Force-sensitive relic by the Jedi Order, and the slow cultural clash is just brilliantly awkward.