Area to use:
I would suggest using the defined base area as a basis for the feature.

Task #1:
Detecting and replacing burnt light bulbs. When you build up your base and there's these ridiculous burn out times for bulbs it's not really fun to be running around replacing 5 bulbs a day.

Maybe you could let the survivors create a bulb on the spot like it is done with the farming water bottle. This would be so nice to have, because I would really like to light up my base more but the replacing is so tedious that I don't turn on some of the lights until its 3am and then only where I am currently going.

Task #2:
Turning all base lights on / off by the same time the natural light would do it. The NPC would go around and turn on / off the lamps in the designated area according to day / night time.

These times should be somewhere in the game. I am talking about the auto lights when the world still has working power. Alternatively maybe there's some info about when the sun sets/rises on the current day and this could be the trigger for the actions.

To mitigate problems with players wanting to keep a certain light on or off and the steward always setting the state like the time demands, you could generate a complete list of objects to interact with once on event start (day / night change) and do not change anything in between.

Task #3:
Opening / closing all windows depending on temperature. This would be done when a threshold is reached for a predefined time period like 2h.

When below the windows could be closed and above they would be opened. This does afaik not change room temperatures but would aid in immersion and give this role more to do.

Task #4:
Carrying rotten food to the composter.

If there's rotten food inside of some container or on the ground and there's composters with capacity available the steward will carry the rotten food to the composter