Great description, makes it a lot easier for me to understand.
I do think that you need to do this in several steps.
1. Use the associations api to fetch the ID of the tickets that are associated between assets and tickets.
Endpoint: read batch of associations
This will return a list of object ids - either all tickets or all assets associated to a ticker / asset.
2. Use thoes ids you got in step one to do updates in properties through out the objects api.
I think simply you are in the wrong place looking. When searching for associations you need to use the associations api (see point 1 above).