How can I let the ray to the edge of the capsule?

When a ray to the player's position hits a wall you could then do a second check with a ray to each side of the player - though you will need a little bit of math to calculate the sides. Note: We're just going to forget about the y position of the objects and think of it as a top down like your image above.

 Vector2 v = new Vector2(rayPos.x, rayPos.z) - new Vector2(playerPos.x, playerPos.z);
 float r = player.GetComponent<CapsuleCollider>().radius;
 
 Vector2 pos = new Vector2(-v.y, v.x) / Mathf.Sqrt(Mathf.Pow(v.x, 2) + Mathf.Pow(v.y, 2));
 
 // convert back to Vector3 for use with your raycasting
 // (Note: the " *r " on the end is part of the calculation, not the conversion)
 Vector3 side1 = new Vector3(pos.x, playerPos.y, pos.y) * r;
 Vector3 side2 = new Vector3(pos.x, playerPos.y, pos.y) * -r;

Then just do a raycast to points Side1 and Side2. Hopefully that solves your issue.