How to fill a large exterior settlement gap between wall and courtyard
Here's the solution I settled on:


Vacuum out the gap to remove debris.
Stick backer rod in the larger gap areas.
Fill the gap with matching grout.


That closes the gap and mates with the settled flagstone.  If there is future settlement, it shouldn't be as much and any new gap will be small.  That can be filled with clear silicone, which will have some stretch if there is more settlement.  The exposed surface can be dusted with the matching grout before it cures to look like the other grout.