I'm sure you understand this, but anonymized data doesn't mean it can't be deanonymized. Given the right kind of data, or enough context they can figure out who you are fairly quickly.
Ex: You could "Anonymize" gps traces, but it would still show the house you live at and where you work unless you strip out a lot of the info.
Now with LLMs, sure, you could "anonymize" which user said or asked for what... but if something identifying is sent in the request itself, it won't be hard to deanonymize that data.