I wrote a blog with Qi Zhu, Jigao Luo explaining how to embed user defined indexes into Parquet files without needing any changes to the format[1].
I am sorry for the somewhat shameless self promotion, but I think this topic may be of general interest to the community in the context of other extensions to the format we have discussed recently. Techniques such as this widen potential usecases of Parquet without any need for consensus or timeline for ecosystem adoption. Andrew [1]: https://datafusion.apache.org/blog/2025/07/14/user-defined-parquet-indexes/