The culprit is the following function:
StackExchange.loadJqueryUi = function() { var cssLink = StackExchange.settings.paths.jQueryUICSSPath , jsLink = StackExchange.settings.paths.jQueryUIJSPath; if ($.ui) return $.Deferred().resolve(); /* Some AJAX loader code... */ }
...which was called by:
$(function() { StackExchange.loadJqueryUi().done(showCalendar); }); function showCalendar() { var $cal = $('.js-daily-access-calendar'); $cal.datepicker({ /* Options... */ }); }
StackExchange.loadJqueryUi assumes that $.ui exists also means $.datepicker() is available, which was not the case. I tried two crude monkeypatches; they both worked:
StackExchange._loadJqueryUi = StackExchange.loadJqueryUi StackExchange.loadJqueryUi = function() { delete $.ui; return StackExchange._loadJqueryUi(); }
StackExchange.loadJqueryUi = function() { var cssLink = StackExchange.settings.paths.jQueryUICSSPath , jsLink = StackExchange.settings.paths.jQueryUIJSPath; if ($.datepicker) return $.Deferred().resolve(); /* The rest... */ }
TLDR: Run delete $.ui in your browser console.
Whether they break anything and how jQueryUI was loaded without .datepicker() in the first place are unknown. I didn't bother to check further, since all I want was to see my SO visit calendar. Isn't she beautiful?

delete $.uiin the browser console prior to trying to open the calendar and have the calendar displayed normally.