On the other hand, instead showing the distances and paths available for displacing a particular token, it should be possible to just dynamically highlight (and to stream to others) the grid cells used for displacing a token,
without adding any automatic calculation on movement costs according to this or that specific game system. This would be simple to add --I think-- and also useful.
Now, I'd like this optionally having into account rotation / facing changes as well, in some way that I can't figure right now, because facing changes very well can be part of movement according to some rule systems.
I think that a distinction between available distances for "walking" and "running" modes is, BTW,
rules specific and non
system agnostic, especially if these available distances can't be customized --which involves complexity: there are systems in which that distinction would be rather pointless and arbitrary, like for instance those just stating that if you use the 50% of your available movement, you're walking, and if you spend the 100% of your available movement in a turn, you're running. Or think about rule systems increasing your available walking or running distance if you burn fatigue points or the equivalent.