When focussed it is possible to navigate the Tool Settings Dialogue with the arrow keys, moving the dotted outline around titles and using SPACE to open dropdown menus or check/uncheck boxes. However, the navigation is inconsistent tool-to-tool where sometimes navigation will get stuck in some settings and navigation is lost. The primary culprit is any tool that gives an option for Fill Colour, such as Place Block.
When using the up/down keys the Fill Colour dropdown opens automatically and navigability is lost. Yes, Left/Right arrows can also be used, but in some tools, such as Place Circle the navigation jams that way too...
There is also no way to expand tools settings, such as Modify Element with keyboard controls.