You opened a tutorial video on YouTube in Safari which is running in full-screen mode. Now in the main YouTube player window, you have clicked on the Full Screen control placed towards the bottom right (of the player). This takes the YouTube video full screen, and moves it to a separate Space of its own.
When you use Command + Tab to switch to Safari, you land on the Safari window running in full-screen mode. You are shown the current Safari tab, but its full-screen video display is on another Space (generally, the next Space towards right of Safari's Space). This is the default behaviour in the described scenario.
After switching to Safari's Space, you'll have to change to the adjacent Space using any one of the methods to change Space. Since you mentioned you don't want to use trackpad, the easiest way to do so, is to use the keyboard shortcut to switch Space. To view/configure keyboard shortcut to switch Spaces, go to System Preferences app → Keyboard → Shortcuts → Mission Control.
The default shortcut assigned by macOS to Move right a Space is Command + →. In my case, I have changed it to Option + Command + →. Command + → is commonly used to move to end of line while editing text, which is a more frequent activity than moving to right Space.