FLUX script not writing new "mapped" data to bucket

Hi,
I got the following issue that drives me crazy :triumph::
With the following script I create 2 new attributes (_timeNew and _timeNew2) and write the final result to a bucket.

import "date"
from(bucket: "ha")
  |> range(start: -1mo) 
  |> filter(fn: (r) => r["_field"] == "value")
  |> filter(fn: (r) => (r["entity_id"] == "m_consumption_daily" and r["_measurement"] == "kWh"))
  |> timeShift(duration: 1h)
  |> aggregateWindow(every: 1d, fn: last, createEmpty: false)
  |> timeShift(duration: -1h)
  |> map(fn: (r) => ({ r with  _timeNew:  r._time})) 
  |> map(fn: (r) => ({ r with  _timeNew2:  r._time}))  
  |> to(bucket: "b1")

After executing the script in the Notebook, the expected result is shown:

When I explore the data subsequentially in the bucket “b1”, the data is there but not the 2 new attributes.

Any idea what the problem might be?
Thanks in advance!