Could always use a VPN to obscure data from the employer.
I wouldn't. In many jobs they view using an unregistered VPN as you are doing something wrong. Even if the policies don't say that, it can get a side-eye.
Pretty sure that's not going to apply in this case.
At work the company offers public wifi after registration with your email.
It's a publicly accessible WiFi, all they could really do is make it a condition of use when you connect to it that you won't use a VPN.
The only way they could enforce it is through traffic analysis I would think.
Doesn't really matter what kind of strange look they give you, they're the ones that provided the free public access. Unless there's something specifically barring employee use and VPNs, they really have no comeback.
Besides, can they really complain when an employee shows good security protocol by using a VPN to access a public WiFi network?
Personally, I've yet to access a public WiFi where I couldn't use a disposable email address and then use a VPN, most T&C are limited to don't engage in actions which are detrimental to anyone else and trying to score a one night stand doesn't really come under that heading.