BD8DIN The spectral "roughness" in the CW signal (at the edges of the on/off transitions) is caused by the sharp edges of the keying signal. This manifests as a "click-click-click-click-click" sound, which is why it's often referred to as a "key click" by non-native speakers.
To improve this noise, you need to control the rise and fall times of the signal edges, and shape the keying signal. This is typically an option available in shortwave radios.
You can refer to these articles:
https://www.rfcafe.com/references/qst/why-key-clicks-october-1966-qst.htm
https://www.w8ji.com/what_causes_clicks.htm
https://web.archive.org/web/20210515173428/http://fermi.la.asu.edu/w9cf/articles/click/index.html
The first two links provide an engineering analysis of issues related to "key clicks".
The last one was an analysis of this phenomenon at a mathematical level (the webpage has been lost; it's being kept alive by time travel technology. I recommend downloading and saving it).
One-sentence version: CW (Continuous Wave) is essentially a 100% modulation AM, and that "noise" is actually the two sidebands (USB, LSB) of the AM signal. It requires additional means to suppress it.