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/utils.ts

@@ -52,11 +52,12 @@ function syncSelectInputUntilChanged(syncData: Array<{ source: string; target: s
     console.error(`The parent selector "${parentSelector}" is not valid.`);
     return;
   }
-  // Set up a single change event listener on the document for handling all source changes
-  parentElement.addEventListener("change", function (event) {
+  // One delegated "input" listener handles every source. "input" (not "change")
+  // makes the mirror live as the user types, instead of only on blur.
+  parentElement.addEventListener("input", function (event) {
     // Loop through each sync configuration item
     syncData.forEach((syncItem: { source: string; target: string; source_value: string; target_value: string }) => {
-      // Check if the change event target matches the source selector
+      // Check if the event target matches the source selector
       if ((event.target as HTMLElement).matches(syncItem.source)) {
         if (!event.target) return;
         const sourceElement = event.target;