Fix add-form JS: name→sort-name sync and related-game disable

Two bugs in the add forms, both root-caused via the e2e harness:

1. add_game Name → Sort name never synced. syncSelectInputUntilChanged was
   scoped to "form", but the first <form> on every page is the navbar logout
   form — the add-form fields live in a later form, so the delegated listener
   never heard their events. Scope to "#add-form" (the add-form wrapper). Also
   switch the sync from the "change" event to "input" so Sort name mirrors Name
   live as you type, not only on blur.

2. add_purchase Related game not disabled when Type == Game.
   disableElementsWhenTrue set `.disabled` on #id_related_game, which is the
   SearchSelect wrapper <div> (a <div> ignores `disabled`). Target the inner
   [data-search-select-search] input instead, so the widget is actually disabled.

Adds two e2e regression tests (live sync; type-game disables the related-game
search input and re-enables it for other types).

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

ts/add_game.ts

@@ -9,4 +9,6 @@ const syncData = [
   },
 ];
 
-syncSelectInputUntilChanged(syncData, "form");
+// Scope to the add form (#add-form), not "form": the first <form> on the page
+// is the navbar logout form, which never contains these fields.
+syncSelectInputUntilChanged(syncData, "#add-form");