How to rotate input based velocity vector based on relative angle of colliding wall so that player moves smoothly?

I have attempted to create a movement system that only uses player input (no physics or rigidbodies), and I want the player to interact dynamically with barriers and walls, sliding across them if the player tries to run against them. I have created a basic flowchart showing how I want to pull this off:

However, the way I have implemented this so far has resulted in strange and glitchy behavior, most notably when trying to rotate the movement vector so the player will travel perpendicular to a wall they are running against.

Here is the script I have (sorry if it's a mess, it's a Frankenstein's monster of forum posts, previous assets, and novel code that I haven't gotten to clean up yet):

 public class PlayerMovement : MonoBehaviour
 {
     public Vector3 dir;
     public Vector3 move;
     public Vector3 normal;
     public float speedC;
     public float angle;
     public RaycastHit ray;
     public bool collision;
     public Quaternion rotation = Quaternion.identity;
 
     // Use this for initialization
     void Start()
     {
         angle = 90f;
     }
 
 
     
 
 
     void Update()
     {
 
         move = transform.position;
         
         //Get input
         var inputV = Input.GetAxis("Vertical");
         var inputH = Input.GetAxis("Horizontal");
         
         //Test for collision with wall
         if (Physics.SphereCast(move, 0.25f, move, out ray, 0.25f))
         {
             Debug.Log("Collision");
             collision = true;
         }
         
         else
         {
             collision = false;
         }
 
         //placeholder vector for input direction
         dir.x = inputH;
         dir.z = inputV;
 
         //determine angle between wall and move vector
         if (collision)
         {
             angle = Vector3.Angle(dir, ray.normal);
             Vector3 cross = Vector3.Cross(dir, ray.normal);
             if (cross.y < 0) angle = -angle;
         }
         else
         {
             angle = 90;
         }
         //debugging variables
         normal = ray.normal;
         rotation.eulerAngles = new Vector3(0, angle, 0);
 
         //slow player down based on the angle of the wall
         float speed = speedC * (angle/90);
 
         Vector3 up = new Vector3(0, angle, 0);
         move.x += inputH * Time.deltaTime * speed;
         move.z += inputV * Time.deltaTime * speed;
 
         //rotate the move vector
 if (collision)
         {
             move = move - transform.position;
             move = Quaternion.Euler(0, angle, 0) * move;
             move = move + transform.position;
         }
         //move the player
         transform.position = move;
 
 
 
     }
 
 
 }
 

This is currently very glitch as it is, phasing through walls and vibrating intensely when up against a wall, as if it's only sometimes rotating properly. If anyone has any insight on how to properly do any of this, please let me know.