Add a new field to document based on the value of the previous with the same correlation id

Is it suitable for log management usage?

You'd need to implement your own life-cycle management policies for entities. Logs are typically stored in time-based indices and retained for fixed periods but entities can span these time periods and need their own retention policy.
You should adopt an incremental update approach to your entities based on latest changes in your event store (aka logs). This thread got into the specifics of how to implement a robust incremental update pipeline for entities.