Now the question is: who's in charge of restaurant inspection on the station? Honestly kind of a Daystrom question.

I feel like on full Starfleet installations (or really any major space-faring entity with bases), with the proliferation of replicators and whatnot, the de-facto health inspection authority is a combination of the Sickbay and Engineering departments, as it just doesn't make sense to have dedicated on-board personnel or send a dedicated ship on a route to inspect food safety at various bases.

However, there's the Bajoran jurisdiction on the station complicating things. You'd wonder how food safety is handled in Bajoran space in general; the list of government departments I found on Memory Alpha definitely suggests it's probably at least de jure someone's job:

• Bajoran Agricultural Ministry
• Bajoran Archaeological Institute
• Bajoran Center for Science
• Bajoran Executive Committee
• Bajoran Freight and Shipping Authority
• Bajoran Intelligence
• Bajoran Ministry of Commerce
• Bajoran State Museum

It could be possible that supply chain safety is usually de jure the job of the Agricultural Ministry (analogous to the US Department of Agriculture), and then there's a Ministry of Health de jure responsible for restaurant inspection (or possibly organizations in political sub-departments, for instance, a Rakantha Department of Health).

Of course, considering the state of Bajor, there's room to be spotty. A lot of this really depends on how unitarian or federalist or the Bajoran government is, although considering the First Minister's control over agricultural policy (particular Winn's actions with Dakhur), I would say the Bajoran government probably leans unitarian.