As of 1.0-19, writing (geo)parquet files doesn't seem to work. It's supported in GDAL, but not included in st_drivers(). This issue is mentioned in an old thread #1756, but I'm not sure what the status is.

st_read(system.file("shape/nc.shp", package="sf")) |> st_write("test.parquet", driver = "GeoParquet") driver `GeoParquet' not available. Error: Driver not available. 

Thanks for your time.