After talking to Twitch Support and other Twitch viewers, it turns out I'm part of an experiment that hides the option to gift a custom amount of subs on the initial screen (you have to proceed to checkout to specify a custom amount). It also doesn't show how many subs you've gifted in the channel on the initial screen (you have to click 'Gift a specific viewer' first).
The fact that an experienced user had to contact support because they thought you outright disabled the option to gift a custom amount should be proof the result of this change isn't as intended. It's annoying and confusing so please don't continue this experiment.