No, the Python bindings are the only available and maintained bindings.
On other suggestion: Have a look at osm2pgsql, more specifically the flex output. It might be overkill for you, but creating GeoJSON from OSM data in a PostgreSQL database is quite easy.
If you’re brave, you might try accessing it via FFI in PHP. Been doing something similar on an old project of mine. As long as you don’t need dozens of calls wrapped, it’s a viable option for PHP. If you need help with that, I might have some time to look into it this weekend.
Update: dealing with objects returned from functions doesn’t seem to be supported properly, so maybe not a good idea
I don’t want to stop you from anything, but wrapping libosmium is really difficult, much more so than for many other C libraries. And libosmium is C++, not C. There is a reason there are no other wrappers available.
Not an answer to your question, but an answer to your use case:
You might want to have a look at leaflet-osm. It can show your downloaded relation xml on a leaflet map directly. No need to convert it to geojson first.