There are games with resal time and tile-based movement (Age of Empires 1, Warcraft 1), but all those I remember are not single character (à la roguelike).
Do you know any game in which you control a single character that has real-time and tile-based movement?
EDIT: I found one example: Real Time Chess https://www.kfchess.com/
Thanks!
I did a quick search and found this video, it may be tile based, but in that case it tries to disguish itself as a more granular-movement system. The tiles are not visible.
For an example of the mechanic, see the EDIT on the post: Real Time Chess https://www.kfchess.com/
Thanks