Okay, on a personal level this can be tricky to calculate and it is highly individualistic.
Example for Heating
A German price comparison site has done the calculation and for their model – 20m² home office and a yearly usage of ~2000 litres heating oil for the whole apartment) – you would end up with ~4% higher usage [0]. That means that you have 80 litres more heating oil which is equivalent to roughly 80 days of commuting 20 km / day via car. The German average commuter does ~32 km / day [1].
The savings from turning household heat down during the day aren't trivial, but they aren't very large either. You can keep your heat ~10-20°F lower during the day when you're not home and save energy, but then additional energy is needed later in the day to get the temperature back up. Typical estimates are that this lowers gas or oil consumption by 10-15%, and only in the colder months. Certainly dwarfed by energy spent commuting, on average.
Your comment on the second+ order effects is much more interesting, but also much more uncertain.
Example for Heating
A German price comparison site has done the calculation and for their model – 20m² home office and a yearly usage of ~2000 litres heating oil for the whole apartment) – you would end up with ~4% higher usage [0]. That means that you have 80 litres more heating oil which is equivalent to roughly 80 days of commuting 20 km / day via car. The German average commuter does ~32 km / day [1].
[0]: https://www.verivox.de/presse/modellrechnung-homeoffice-erho...
[1]: https://www.postbank.de/themenwelten/beruf-vorsorge/artikel_...