Excatly this ist the problem and also a bug in REVIT, see as reference the following posting from @hazem.adel: Re: Verschachtelte Familien in Baugruppen verwenden und anzeigen - Autodesk Community - Internationa...
Translation of the main post:
yes now it is clear and I know this problem in Revit or let's call it a bug.
If you select the assembly and then edit it, you can add something to the assembly and select the other parts or nested families, this works but if you have many assemblies, unfortunately it takes too long.
Accordingly, I recommend solving the problem with Dynamo. You can write a little dynamo code to assign a parameter to the different nested families, which is then automatically added to the assembly.
It's not complicated, I wish I had time to write it for you.
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BR Peter