>>55752836Snap but you catch them is an interesting concept. Apples and pester balls or similar could lure them out as well as work like baits and rocks. But what part of the old way wouldn't work in 3D?
Steps? Sure there aren't tiles but the player model takes steps, or whatever units of distance the game already uses as a "step" while on a bike or ride Pokemon for egg hatching, incrementing friendship values, etc. Or they could use a real-time timer like the Johto bug catching contest.
Random encounters now that they're all visible in SV? They could either use a gimmick like putting long grass everywhere so you couldn't reasonably see the Pokemon in it, and have random encounters there. Or they could let you see them, it still takes steps to do it this way because you have to walk to make old ones despawn and new ones spawn.
A battle but without your Pokemon model and just ball/bait/rock/run options could work as-is. Though it'd be much more fun to have it all in the overworld, with a Zelda style Z-targeting system to help you aim your balls, baits and rocks in the usual 3rd person view the games use. When they flee they just run away from you, you can chase after them, and then they're gone if they either reach the despawn distance or run into a hole or thicket. Bait could distract them if they're fleeing but lower the catch chance, and rocks could raise catch chance but also have a high chance to make them start running.