I was still thinking of using the SVG as a static graphic, not editing the music.
SVG can contain text, and according to the Dorico documentation, SVG export retains a fair bit of text (it doesn’t specifically mention lyrics, but that seems to be the sort of thing that might remain editable text).
I was thinking you could choose font you wanted for the alphabetic text elements in the SVG, and use the exported paths for the musical symbols (which would, as you state, no longer be editable as notes, although they would be editable as vector shapes for colouring, outlining, Boolean effects, etc), but if you want to use a font for the musical note symbols, no, I agree that would not work.
I suspect using a general vector editing app might not be the best path if you want to retain editable musical note symbols.
The full Bravura font is available.
However, because this font (and similar implementations) is using Unicode’s Private Use Area to encode the musical symbols, rather than being part of the standard Unicode character range, I’m not sure how many apps (if any) will support the musical symbols in such fonts, unless the app is written specifically to be compatible for music editing.