Could someone shed some light into a method to link breaking outline borders without much distortion from the original like e.g. convex hull does? Convex hull alternative ideas are of course welcome to be tried even if they have similar results.
You could do an old-school buffer-debuffer technique (discussed many time on this site e.g. here and elsewhere too) followed by hole removal. The key here will be the amount you buffer-debuffer by. By looking at the second image I'd go for about 2 or 3 times the raster resolution.
Alternatively you could try using a concave hull tool (aka alpha shape). This is like a convex hull but a lot tighter. To find this simply type 'concave' into the Processing Toolbox search and it'll pop up in Qgis 3.x (earlier version need a plugin to be installed). It's under Processing Tools->QGIS Vector Geometries and you'll find a couple of options to try. It'll all depend on your tolerances etc.