Does centrifugal force actually exist?

IS THRERE REALLY SUCH A THING AS CENTRIFUGAL FORCE?

I came across a physics textbook which says centrifugal force is that force which keep an object away from the centre of the circle, but is there really such force?
Let us consider a mass tied to a rope and whirled horizontally in a circular pattern as illustrated in the figure below.

If the mass is whirled such that it has a constant speed, it can therefore be said that the mass has a constant speed but not constant velocity because velocity is a vector quantity and it depends on the direction of motion, therefore a body moving in circular orbit does not has a constant velocity because its direction changes constantly. In other words the body accelerates because acceleration is the rate of change of velocity and the acceleration of the body is always towards the centre of the circle because the tension on the mass is always acting towards the centre of motion. The velocity of such mass at any point is always tangential to the rope or its orbit as shown in the diagram above.
This can be understood by assuming there is a breakage in in the rope at a particular point as illustrated in the diagram below.

The mass will be seen to move tangentially to the rope or orbit not outward from the centre of the circle, because at the point of breakage the mass will now have a velocity tangential to the orbit, that is, the mass will now move with a constant speed or velocity in a straight line in the absence of other forces. Because according to Newton's first law of motion "The inertia of a body is to be at rest or continually moving in a straight line"
A friend once ask me "What about the force we feel in our hand which makes it look as if the mass is trying to move out of the circular orbit". Yes, we actually feel a force in our hand which seems like the mass is trying to pull out of its orbit. But the force you feel is as a consequence of Newton's third law of motion which says "For every action there is an equal but opposite reaction". Therefore the force we feel is as a result of the force we exact on the mass trying to make it move toward the centre of the circle, that is, the tension we exact in the rope trying to make the mass accelerate toward the centre of the circle has an equal magnitude of force acting in the opposite direction which makes it look like centrifugal force as it is called.

Also, a car moving in a curve path is kept towards the centre of motion by the frictional force on its tyre. Let us assume the car gets to a spot along the curve path which is perfectly smooth(frictionless), the car will not accelerate away from the centre of motion but move in a straight line tangentially to its curve orbit as illustrated by, v in the diagram shown above. The car will tend to move in a straight line to acquire its state of inertial and not away from the centre of motion.
There for I believe there is no such thing as centrifugal force, except for the situation of a second force which is exacted on a body subjected to a circular motion away from its centre.
images credit

My name is Hydro, I just gave my idea and I really love science💝