I am self-employed having an office in DC. Because of COVID, I have used home office in 2021. If I deduct home office expense, am I subject to county business tax?

We aren't really experts on local tax laws. 

To take the home office deduction, you must use your home regularly and exclusively for business.  (Here, exclusive means you use part of your home for business and do not share that part of your home with any personal use.). If you have more than one place of business, your home must also be your main place of business to use the home office deduction.  It would be acceptable for it to be your main place of business in some months and not others, if you pro-rated the expenses, but your home must be your main place of business.

While I have not read the Virginia business law you reference, it stands to reason that if your home is your main place of business, you owe whatever taxes and fees you would owe if your main place of business is in VA.

https://www.irs.gov/publications/p587#en_US_2021_publink1000226302

https://www.irs.gov/taxtopics/tc509

TurboTax does not handle local or county taxes so you would need to contact the county tax assessments office to find out if you would be subject to that particular tax.