There are dual source (gas & heat pump) furnaces now that can run the heat pump side down to -5° F outside temperatures, and still have a COP greater than 1. Then most all of your shoulder season heating could be done that way, with the gas backup for when it's really cold.

I'd find an online calculator for BTUs/$, and compare the cost for Heat pump vs gas.

Plus the IRA has some good tax credits for upgrades.

I'm looking at this one for our rental. https://hvacdirect.com/1-5-ton-14-5...-and-heat-pump-system-upflow-133745.html

Page 19, find the COP row, with outdoor temperature in each column. https://hvacdirect.com/media/pdf/GSZH5%20Spec%20Sheet.pdf

Good overview of heat pumps in chicago (cold!). https://youtu.be/MFEHFsO-XSI?si=7qBNw_obpEmUAMhI&t=516