Use methods of Transform without linked gameObject

So i'm looking for the functions similar to those on the Transform class on an object that I can easily set and get in my own scripts. I think the API of the Transform class is really clear and easy to understand as opposed to the Mat4x4 which seems more linked to the mathematical terms.

I would rather not wrap up the Mat4x4 class that acts similar to the Transform class, like so:

 namespace Math {
 
     public struct MatTransform {
 
         public Matrix4x4 mat;
 
         Vector2 right { get { return this.mat * Vector3.right; } }
         Vector2 left { get { return this.mat * Vector3.left; } }
         Vector2 up { get { return this.mat * Vector3.up; } }
         Vector2 down { get { return this.mat * Vector3.down; } }
 
         Vector2 TransformPoint(Vector2 vec)
         {
             return (Vector2)mat.MultiplyPoint3x4((Vector3)vec);
         }
         Vector2 TransformDirection(Vector2 vec)
         {
             return (Vector2)mat.MultiplyVector((Vector3)vec);
         }
     }
 }

And the rest of its methods.

In short, I don't want to instantiate a gameObject and access its transform. But I want to store a local transformation space within my script and access/change it with the functions as are on the Transform class.