Value template works in Dev tools but error in config

Configuration
3

What finity said; in the future, please follow the guidelines in the forum’s FAQ.

The problem is due to the fact the template lacks outer quotes.

sensor:
  - platform: template
    sensors:
    
      washing_time_finished:
        friendly_name: 'Washing Time Finished'
        value_template: "{{ as_timestamp(strptime(states('sensor.washer_washer_completion_time'), '%d %m %Y %H:%M:%S')) | timestamp_custom('%d %b ~ %I:%M', false) }}"

Alternately, you can use the line-continuation character and move the template to a separate line. Then it doesn’t need outer quotes.

sensor:
  - platform: template
    sensors:
    
      washing_time_finished:
        friendly_name: 'Washing Time Finished'
        value_template: >
          {{ as_timestamp(strptime(states('sensor.washer_washer_completion_time'), '%d %m %Y %H:%M:%S')) | timestamp_custom('%d %b ~ %I:%M', false) }}

NOTE

Please note that the corrected examples I posted use single-quotes within the template and double-quotes outside the template. You can also do the opposite (double inside, single outside); whatever you use outside, don’t use it inside. Your original example used both single and double-quotes within the template.