Some companies have a proprietary file format for compressed 4D Gaussian splatting. For example: https://www.gracia.ai and https://www.4dv.ai.

Check this project, for example: https://zju3dv.github.io/freetimegs/

Unfortunately, these formats are currently closed behind cloud processing so adoption is a rather low.

Before Gaussian splatting, textured mesh caches would be used for volumetric video (e.g. Alembic geometry).