I have recorded a demo video that seems to be validating my point.
The video is recored on a fresh install of Youtube on iOS 13.2.3. That means I uninstalled and installed the Youtube app. The demo that you would see is on the very first launch of the app.
Here is the timeline, also posted on the video description.
0:04 I am logged into my personal account. You can see Formula 1 video suggestions because I tend to follow Formula 1 quite a bit
0:10 I switch to incognito mode in Youtube. The popup says that once incognito is turned off, my activity from this session will be cleared. At this point, suggestions in incognito seem random to me
1:00 I search for Formula 1 while in incognito mode
1:26 Quit incognito mode. At this point, I believe that my session is cleared
1:35 I switch to incognito mode again. My video feed seems to be heavily skewed towards Formula 1 video suggestions. This holds for subsequent incognito mode activation as well