Okay, so I've been in the Genshin fandom since launch and the Venti/Aether ship really took off early—partly because they're two of the first major characters you meet who aren't actively trying to kill you. The dynamic people latch onto is pretty clear: the chaotic, ancient archon bard and the earnest, kind-hearted traveler. A lot of fics play with the 'god hiding in plain sight' trope, where Aether either figures Venti out early and keeps the secret, or is hilariously oblivious for ages while Venti drops increasingly unsubtle hints.
There's also a huge amount of 'found family' or 'wandering together' stuff. Since both are technically rootless travelers (one by choice, one by circumstance), a common plot is them deciding to journey across Teyvat as a duo. It lets writers explore the world through their banter, which is always fun when you pair Venti's playful teasing with Aether's more grounded reactions.
Angst-wise, you see a lot of fics touching on immortality and memory—Venti's long lifespan versus Aether's unknown timeline, the fear of being forgotten, or Aether trying to cheer Venti up after he gets melancholy about his old friends. Hurt/comfort is massive here, often with Aether being the steady anchor. And, of course, the classic 'Venti gets seriously injured protecting Aether and his godly nature is revealed' scenario never gets old.