High Frequency Collision Checking

For collision checking (running at high frequency), would something such as Region3 or GetTouchingParts or a multitude of magnitude checks be preferred? - For example: something like a “pet” using an animation controller, following a player. When the player walks up on the sidewalk the pet Y axis also changes (say movement is changed via tweening).

Or another example… simple placement system, checking collisions to see if desk can be placed without colliding with a fridge as the player’a mouse moves around to place etc.

I’m curios to see other’s thinking and approaches people would take to make the quickest/most accurate systems! - Don’t need any exact code, this is more just to brainstorm best methods!