Move legacy request helpers (#2829)

In #2698 we decided to put legacy helper functions in `core/legacy`. I think that’s a fine idea, though if we’re going to have a bunch of badge helper functions in there, it seems like it is probably better to keep these two important but esoteric helper functions with the core code to which they are most coupled. So I added `legacy-` to the name, and put them in `core/base-service`.