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Alright, just dropping this in here to hopefully clear some of the weirdness about how the crown things work.
This was my DexNav in Route 118 at various points in the game. I got lucky enough to catch it right before I got the silver crown for it, so that makes it easier to see how this works.
According to Serebii, here are how the wild mons break down:
Grass: Linoone, Electrike, Wingull, Pelipper, Kecleon
NatDexNav: Raticate, Aipom, Luxio
Fishing: Magikarp, Tentacool, Carvanha, Sharpedo
Surfing: Tentacool, Wingull, Pelipper
At the Bronze, I had all the Surfing mons, but missing one of the grass mons and one of the surfing mons. When I got Kecleon, it became Silver. And then when I got the last Fishing mon, Sharpedo, it became Gold. After getting all the National Dex mons, it became Platinum.
Based upon this, you get one level of crown for each area (grass, surfing, fishing) completed. In caves, the cave floor replaces grass. If there's only two areas, it skips silver, and if there's only one, it skips bronze. Notice, not seeing the last fishing mon had no affect on the crowns, so I'm pretty sure it's just marking the things you caught, not seen. Not sure how this cross over to DexNavs on the water, but I'm not sure those even exist, but I'd imagine they work the same as here: Gold for when you've caught everything pre-NatDex across all the areas, Platinum for when you've caught all the national dex mons and everything else.
No idea if these crowns do anything besides convenient mark, in game, if you've caught them all on the route. And look super sparkly at the last level.