Any APIs or apps that allow for complete keyboard navigation OS-wide, including inside apps
macOS has a variety of apps like Homerow, Shortcat, and KindaVim (watch the videos in those links if u can) that allow for navigation of apps using just the keyboard. Homerow allows for pressing a hotkey and then showing letters over UI elements which can be entered to move the mouse to said element, similar to the Vim easymotion plugin. KindaVim attempts to implement vim modal navigation inside GUI apps, so you can enter normal or visual mode and use j and k to move up or down. They all work using macOS' accessibility API which exposes UI elements for programmatic interaction.
I did a bunch of searches for Linux equivalent of such apps and Mac's accessibility API, and didn't find anything as comprehensive. Can you navigate a wide variety of Linux apps using mostly or only the keyboard (apps made with GTK, Electron, etc.)? Is it currently possible to develop an equivalent of the apps listed above?
I don't know of a universal tool for adding keyboard navigation to all the different GUI toolkits used on Linux. I wouldn't expect one to exist, since each toolkit implements its widgets differently, just as the Windows and MacOS GUIs implement theirs differently.
However, apps made with Qt tend to be good at keyboard navigation already, which is no surprise, since support for it is built in to the toolkit. The KDE Plasma desktop environment inherits this support, as do most of the apps made for it. I suggest trying it if you haven't already. (Hint: Many widgets will reveal their keyboard shortcuts when you hold down Alt, and a Settings: Configure Keyboard Shortcuts menu item is very common in KDE apps.)
Tangentially related: You might also want to look at tiling window managers. Some people love them.
This isn't a Linux thing exactly, but I know the QMK firmware for keyboards has a feature called "mouse keys" that let you control your mouse cursor and click and scroll and such exclusively via keyboard keys.