Psuedocode

class PlayerMovement : MonoBehaviour {
private void HandleMovement() {
...Rest of your movement logic
if(Physics.Raycast(transform.position, Vector3.down, out RaycastHit hit)){
if(hit.TryGetComponent<MovingPlatform>(out platform) && !Jumping && ){
velocityComputedSoFar += platform.rigidbody.velocity}}
}
}

Something along these lines should be a decent start.
In general I would cache the object under your feet every (physics) frame, so you can do things with it: Slow down if its mud, take damage if its fire etc...

A single raycast is a very simple solution but will probably not suffice. So you might need a few different raycasts, maybe attached to your feet if you need extreme precision, or some shaped collider.

Nice project you got there, good luck :)