Thanks for the update!
I tried OOoLilyPond v1.1.6 beta on Fedora 36 with Libre Office and the new Cairo backend seems to work nicely with it. Note for other Fedora users: The lilypond-2.23.12 that is currently packaged in the Fedora repository has been compiled without the cairo backend and will not be capable to use this new functionality. It was easy to compile my own RPM package version using the Fedora specfile. I just needed to add --enable-cairo-backend to the configure options. Now I can enjoy SVG support with the Cairo backend in OOoLilyPond.
MT