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Isn't it a bit weird to launch a "never delete anything" store today and not mention anything about European GDPR requirements?

How would you go about deleting a users data upon request?

You delete it. It's still a database. What's being done here is just smart partition management as an extension to Postgres, similar to CitusDB.

You can also use any column-oriented relational database with a time-based partition key and do the same thing.