URL generation logic is complex and we should handle configuration like
basepaths and the use of trailing slashes in a central location to avoid
simple, but hard to find mistakes.

This change also gets rid of the VUE_APP_API_STEERING_SHOWS env
variable, that is just a 'shows/' suffix of the VUE_APP_API_STEERING env
variable.

We use a script to update variables at runtime that usually can only be
injected at build time. Since we’ve migrated to Vite as build tool the
paths the string substitution has been performed on have changed.

The paths have now been updated and should be future-proof, as we take
the whole dist directory into account.