Rather than getting hung up on frontend vs backend, it would be worth considering what the architecture for your UI looks like.
There are a number of common paradigms for user interface architecture. Model-View-Controller is probably the best known (although the name is often mis-applied to other architectures), with other related paradigms like Model-View-Presenter, Model-View-ViewModel, and the loosely related Flux paradigm.
What most of these paradigms have in common is that they separate business logic (model) from presentation logic (view). They differ in how these components are connected, and what supporting infrastructure assists with this, but that is a key characteristic that they all share.
Assuming you're following a paradigm like this, probably the most important thing to recognise is that culture isn't part of the business logic, so doesn't belong in the model. Depending on your exact paradigm, it might make sense for it to live in the view, or in one of the supporting components (localisation is not an unreasonable thing to handle in a ViewModel, for example), but you probably don't want it in the model.
In terms of web application architectures, there's been a shift in recent years, where the model used to live purely in the backend, but nowadays is more likely to live in the frontend, or at least span the two (and paradigms like Flux attempt to make this more concrete). So depending on your application, it may make sense to put the localisation logic on either side of that divide. But the guiding factor should probably be the architecture. Where is your model, where is your view, what connects them, and what is responsible for what?