MS Word: Preserving vector graphics (SVG) when saving document as PDF
Microsoft seems to have improved SVG support in Word. SVG vector graphics are now perfectly preserved when saving the document as PDF.
(I'm using Office version 1806)
In response to your final question:
"If this is only a SVG issue: Which other vector graphics format will work better?"
For years the only vector format that Word supported was Microsoft's proprietary .emf file format. If you encounter further issues, you can always try converting your .svg to .emf. Inkscape can export as .emf, and in my experience it's a much more accurate conversion than Adobe Illustrator.
Incidentally, the workaround that Andrew posted above works by converting your clipboard data into an .emf file. However there are a few times when exporting from Inkscape directly would be preferable, for instance when you want to preserve a buffer of blank space around your graphic (using the clipboard will not select blank space).