Man, crossing over Pokémon with anything else always puts trainers on a weird power scale, and shiny Umbreon's a perfect example of that puzzle. It's not just a pretty dark-type, that whole moonlit evolution thing gives you lore hooks you can hang other worlds on. I wrote this awful 'Pokémon in Westeros' thing ages ago, and the shiny Umbreon worked as a direwolf stand-in for a Stark kid, but also its rings glowing in the dark had some spooky weirwood connection? The plot was a mess, but the aesthetic clicks.
Where it fits best, honestly, is in moody urban fantasy or sci-fi crossovers. A sleek black creature with golden markings moving through a 'Blade Runner' neon-soaked cityscape, or as some fey creature's familiar in a 'Dresden Files' style magic system—it's visually built for that. Less about battling and more about being this elegant, silent guardian that bridges the normal and supernatural elements. I've seen a shockingly decent 'Pokémon x Persona 5' fic where a shiny Umbreon was the protagonist's Persona, the rings shifting like a mask. The symbolism of light in darkness, or beauty in something typically 'evil' typed, gives writers a lot to play with beyond just stats.