When I logged in to support.apple.com and search for the nearest service provider, it said it is not possible, as I expected. My location services are turned off since Day 1. There is no particular reason, I just do not need that for the device in question. Only one device is added to the particular account, and I never really carry this device to anywhere.
I remember to have search up my zip code once (on the support website to get the nearest provider) which probably might be available to them (albeit unlikely), or they probably have the data because of the details provided by Apple Store from where I purchased it.
It freaks me out, since I do not see something that they see. Not because they have the details.
Best Answer
There could be multiple sources that Apple has received your location from.
Even if you do not think about it, your IP addresses is actually transmitted to the web server (Apple's server) every time you load up a web site. In many cases an IP address can pinpoint your location to a specific city or similar. This would be enough for them to able to suggest a store in a specific zip code.
In addition WiFi-enabled devices without GPS are still able to find their location from other sources - for example the names (SSIDs) of WiFi access point the device "sees". When it is moved around, it is possible to assemble a list of known access points which can then be translated into a position by an online server. For example the cars that Google uses to gather data for Google Maps also collects WiFI SSID information for this purpose.
If you're especially worried that Apple support knows your location, I would just ask them where they have your address from. If you're located within the European Union, you have rights based on the GDPR that would ensure that they're obligated to tell you that they have this information on file.