tl;dr: The value you are looking for depends on the clutch design, is constant in power for the most common type of manual clutch and only really affects the gear shifting sound anyways.
Nothing in the physics world is discontinuous, but the engine axle is just a short rod inside the engine, a couple of cams inside the engine and a disc inside the clutch. It doesn't have enough inertia to affect how a car feels when driving. Its angular acceleration is greatest when changing gears, not during braking.
The angular acceleration when shifting gears is then governed the moment of inertia of the engine axle and by the clutch design (more friction = less service life for the clutch). The angular acceleration when revving up is governed by the moment of inertia and the engine torque. The angular acceleration when idling is governed by the moment of inertia and the friction from bearings. When the clutch is fully engaged, the engine axle's rotational inertia becomes insignificant. If your car uses automatic transmission, you can ignore all three of these values.
When the car accelerates, the acceleration is governed by the car mass (plus cargo) and by the engine torque as a function of its current speed (RPM) and the amount of fuel flow (normally you measure maxTorque(RPM) and then fit a curve onto it) and by the transmission ratio.
When the car brakes, most of its deceleration is comes from the friction between the tires and the road (dependent on both the tire and the road surface). Car's ability to break doesn't depend on its speed or the engine power. There's an electronic system that prevents the brakes from applying too much friction between the wheels and the braking mechanism. The same number also applies when the car accelerates.
When the car coasts, its deceleration is determined by air drag (quadratic function of the speed) and its tires' rolling friction (function of road surface and car type). These two forces also help braking and reduce acceleration.
Sources / useful links:
https://www.caranddriver.com/news/a15347872/horsepower-vs-torque-whats-the-difference/ (contains a typical torque and power curve)