First off, I can tell you there's no official
Game released by Nintendo or The Pokémon Company that wears the exact name 'PokéWars' as a
Crossover brand. That doesn't mean the idea doesn't exist in other forms — Pokémon has definitely been mixed with other game styles and dev teams in official, licensed ways. One of the best examples that scratches that same itch is 'Pokémon Conquest', which basically fused the Pokémon formula with the tactical, historical-war vibes of Koei Tecmo's style — it feels like a strategy war game that happens to have Pokémon as your troops and generals. That was an actual, official collaboration and it leans right into the “poké-wars” concept.
Beyond that, there are titles where Pokémon characters meet other franchises or engines: 'Pokkén Tournament' was built by Bandai Namco and uses fighting-game sensibilities familiar to fans of other fighters, and the 'Super Smash Bros.' series is a longstanding multi-franchise
playground where Pokémon fighters and Poké Balls interact with characters from dozens of other series. These are official crossovers in the sense that The Pokémon Company and Nintendo sanctioned them, even if they don't use the word 'PokéWars'.
If you love the war- or strategy-focused mashup idea, 'Pokémon Conquest' is the most on-point official example; otherwise, look to 'Pokkén Tournament' and 'Super Smash Bros.' for legit cross-franchise action. I still get a kick thinking how strange and fun it is to see Pokémon transplanted into totally different genres — feels like someone opened a toybox and mixed everything together.