Input shaping is one of those 3D printing terms that sounds way more complicated than it really is. On the Centauri Carbon, it's basically there to compensate for vibrations created when the printhead is flying around at high speeds. The end goal is cleaner prints with less ringing or ghosting around corners and other sharp details.
The Centauri Carbon has automatic vibration compensation, so for most people, I really wouldn't mess with input shaping manually right out of the box. Let the printer run its calibration and see how your prints actually look before you start trying to fix something that might not even be a problem.
You'll usually notice an input shaping problem as repeating lines or shadows next to sharp features on your print. For example, if you print something with raised lettering and you can see faint copies of the letters continuing across the surface, that's the type of ringing or ghosting input shaping is designed to help reduce.
One thing I would definitely do is recalibrate the printer if you move it. The table or surface your Centauri Carbon is sitting on can affect vibration, especially with how fast these newer CoreXY printers move. If you move the printer from a heavy workbench to a lightweight desk that shakes around, I'd run the calibration again.
The same goes for making bigger changes to the machine. If you've messed with belt tension, worked on the motion system, or changed something that could affect how the printer moves, running the vibration calibration again is an easy thing to do.
I also wouldn't automatically blame input shaping for every little imperfection in a print. Belt tension, loose parts, acceleration, filament, extrusion, and even the model itself can cause issues that look somewhat similar. If your Centauri Carbon suddenly starts producing ringing when it printed perfectly before, I'd check for something mechanically loose before going crazy changing settings.
For most Centauri Carbon owners, this is really one of those features you can let the printer handle. Run the automatic calibration, put the printer on a solid surface, and start printing. If you're getting clean prints without noticeable ringing or ghosting, I'd leave the input shaping settings alone and enjoy the printer.