You can also look at 'Define Property Sets' this allows you to extend the data attributed to your model elements. You can fine it under Manage > Property Set Data > Define Property Sets.

The EIR for this project requires the Floor & Type fields; I use the set COBie_General to apply a property to all elements, currently I have this set for COBie.ExtSystem with a default value set to 'Autodesk Civil 3D 2022'. COBie_Floor is set to only apply to 'Surface' object and the COBie_Type is set to 'Pipe' & 'Structure' objects; these will be defined in your projects EIR.
However, there is a limitation as you can't apply Facility or Contact data to the whole model like you can within Revit via the 'Project Information' category. You could easily create a COBie_Facility & COBie_Contact data sets and apply these to all elements, you'd need to make sure you add default values.
The properties and thier values can be viewed or changed in the 'Properties' window.

The downside with the property sets is you can't save them to import into your projects but, you scan define them once in your template file for use on all projects. I haven't tried the 'Import' feature found at Manage > Styles > Import so it could be possible to bring them in that way,
Another thing to turn on before starting this is the AECPSDAUTOATTACH this will automatically apply the Property Sets to your selected Object/Styles when you press apply,