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!
Never tried DnD - but is it tile-based? If so, Baldur’s Gate and related games might count.