The way I would do it.

Use, forgotten the term used, melted down with cement gooey plastic.

It slightly melts the side of the gap, just as cementing pieces together. Will not crack.

Tried it years ago. CA does not have the same tensile strength & is liable to crack

away from the plastic..

The filler , also being plastic, it will take for instance Mr Surfacer 500 to fill over the top & above the crack & sand down well being of a similar hardness.

Laurie