My town doesn't care if you operate a business from your home as long as you don't have customers visiting or frequent deliveries in a residential area, they just want to make sure they get their tax revenue! There are some additional restrictions if you have employees working there, but a large number of businesses in my town are operated from someone's home.That's a good concern. There's a lot to be said for staying below the radar.
24 years ago when our daughter was born, I lost my home office to the crib and changing table. So I rented a 1-room office a couple blocks away... Landlord was a super nice guy. Upon giving me the keys, he told me to watch out for the "city lady."
The "city lady" was a civil servant with seemingly no other job than sniffing out self-employed smucks like me, operating within city limits without a business license. She's was a master at finding every new LLC, DBA, tax ID change of address, etc. He said she would periodically make rounds knocking on doors of all the small office properties in the area looking for new tenants. She'd act like a friendly neighbor asking about where you were from and what you did. Once she learned enough to know you should have a business license, she'd ask to see it.
"Best to just not answer the door," he said.
Here in CT, local towns get their tax revenue from businesses though "personal property tax", ie. they tax any and all assets of the company down to how much you spend on office supplies each year. The state sends them a list of corporations and LLCs registered in the town every year, and they have the list from the town clerk for those that registered a DBA, so the tax collector only needs to try and find the ones that are operating unregistered. Google is making it easier on them by populating their mapping software with businesses it finds while crawling the web for company listings, and I am sure social media posts are being cross referenced as well. It's getting harder to operate under the radar, but people keep trying to do that.
Your situation of renting an office instead of a home office got me thinking of all the people working remotely, I could see my town considering your employer having a presence in town by working from home and requiring them to register with the town, and pay tax on any assets you use there. If you have a company car that you drive to and from your home each day, that gets the personal property tax assessed in the town you live in even though you do not own it, so the same might be true for someone that works remotely with a home office.