That does seem pretty noisy and/or grainy for Super 16mm 200T. As a reference, here's something I shot on 200T 7217 Vision2 stock in regular 16mm years ago, which still seems much cleaner: https://vimeo.com/20427663. Telecine'd in HD on a Spirit Datacine, which is a pretty old machine.
There are a number factors that could cause grainy or noisy footage - underexposed negative, old filmstock, overdevelopment (push processing), the scanner itself, and color grading.
The negative looks pretty well exposed based on the scan. What ASA did you rate the film at? Did you intentionally over/underexpose at all? While an underexposed negative will create grain in the shadows and mids on the film, an overexposed negative may create noise in the highlights of the scan due to the scanner's backlight struggling to get through a dense neg and expose the sensor. But we're not seeing that here.
How old was the film? Did you store it in the fridge or freezer? How long did you wait to get it processed after shooting? Was it subjected to extreme heat at any point prior to processing?
Was it processed normally or push/pulled?
Which scanning machine was the scan done on? Some emphasize grain more than others, others have less latitude which may increase noise. The first image you posted doesn't really look like Cineon Log to me, the red is too saturated and I would expect it to look flatter in contrast. If the scan was already graded, and then you pushed the saturation further, then that could create more noise.
Here's a 2K 35mm Log scan for comparison (please excuse the jpeg compression of the stills):
Corrected with only Contrast Curve and Saturation Boost:
Color Corrected with Lift/Gamma/Gain:
As for what to do now, since you're mostly seeing blue grain/noise in the shadows, you could try crushing the blue channel by pushing the shadows slightly toward yellow if you want to get rid of the noise.