Can I include the cost of a new furnace and air conditioner as repairs and maintenance? In 2019, I replaced both units and I write off part of my home as a home office.

No. They are assets that must be depreciated along with your house. You can only take a deduction for the business use portion, which is determined by the square footage.

A repair would be to fix a furnace/ac, not purchase a new one.

I understand that they have to be added as assets. But Turbo gives categories of asset that are pretty limited. Should I select: "Tools, Machinery, Equipment, Furniture" or "Computer, Video,  Photo, Telephone Equipment", or "Real estate property?"   

Select

"Tools, Machinery, Equipment, Furniture" 

Real estate property itself cannot use Bonus Depreciation. 

Only the assets ADDED may.