Models on QGIS 3 are stored following a XML schema. Do you know if it is possible to embed metadata, may be using Dulin Core or ISO? I have noted that the modeler's help take in account subjects like: author, version, documentation and so on. But I am not sure how to include metadata information on .model3 files.
Not 100% on this but I think metadata is a work in progress, being approached from a number of angles.
If you have metadata to save, apparently it can be saved to a file which sits in the same directory as the data. As per this answer QGIS Default Metadata
If you are trying to read existing metadata from another system (your case) I presume QGIS is expecting to read a *.qmd file.
There is a plugin which apparently used to help some users, but apparently it no longer works with updated version of QGIS. https://github.com/nextgis/metatools/issues