Catalina Keyboard shortcuts preferences missing 'full keyboard access'

vs.

I am not sure why I do not see this option. I want to see this option because I have for long since been in search of the hotkeys to enable navigation through search results without a mouse click.

This seems to be the only option possible without using a plug-in, unless I'm mistaken?

It was quite difficult to find leads to (enabling toggling between search results!!!) it, the link that explained the relevant information of what I desire are here for instance.

The UI was simply changed in Catalina. In Catalina, ticking "Use keyboard navigation to move focus between controls" is identical to selecting "All controls" in Mojave. Unticking "Use keyboard navigation to move focus between controls" in Catalina is identical to selecting "Text boxes and lists only" in Mojave.

You can confirm this using Terminal in both versions of macOS and seeing what changes in the output from defaults read (redirect the output to a file and diff the two files). Switching between the radio buttons on Mojave and enabling/disabling the checkbox on Catelina both only change the following preference:

defaults read "Apple Global Domain" AppleKeyboardUIMode

When "Use keyboard navigation to move focus between controls" is ticked (or "All controls" is selected) the value is 2. When "Use keyboard navigation to move focus between controls" is unticked (or "Text boxes and lists only" is selected) the value is 0.

This has nothing to do with full keyboard control. To make focus move to search results instead of just moving around controls the default shortcut is to use option + tab. You can also change this behaviour in Safari preferences -> advanced -> press tab to highlight each item on a webpage as show in the attached picture.