fix(filters): builder UX round one — incomplete rules, group removal, field menu (user report)

- Root bug: incomplete rules (the ready rule, every new group's first
  rule) were sent to the server — the live-count fetch toasted a 400
  and every suggestion fetch failed silently (why author typing showed
  no dropdown). Fix: completedTree() prunes incomplete rules and empty
  groups; the count fetch skips when nothing is complete, suggestion
  fetches send only the other COMPLETED rules, and serialization wires
  only completed rules (an unfinished rule was never a filter).
- Group remove button was x-show'd away on depth-0 groups — exactly
  where user groups live. Always visible now.
- Field menu: filter input at the top (Enter prevented), no-match
  state; group headers restyled as flush-left tinted sticky bands with
  options tabbed in beneath (user's layout pick).
- toast.ts: filter-count fetches join the suggestion-fetch exemption
  (a failed background hint never interrupts).

templates/bookshelf.templ

@@ -189,7 +189,7 @@ templ BookShelf(
 													<span class="flex-1"></span>
 													<button type="button" class="fb-mini-btn" @click="addRule(row.path)">+ rule</button>
 													<button type="button" class="fb-mini-btn" @click="addGroup(row.path)">+ group</button>
-													<button type="button" class="fb-mini-btn fb-danger" x-show="row.depth > 0" @click="removeNode(row.path)" aria-label="Remove group">×</button>
+													<button type="button" class="fb-mini-btn fb-danger" @click="removeNode(row.path)" aria-label="Remove group">×</button>
 												</div>
 											</template>
 											<template x-if="row.type === 'rule'">
@@ -199,7 +199,10 @@ templ BookShelf(
 													<div class="relative">
 														<button type="button" class="fb-picker" :class="{'fb-picker-active': row.rule.field !== ''}" @click="toggleMenu(row.key + ':field')" x-text="fieldLabelOf(row.rule.field)"></button>
 														<div class="fb-menu" x-show="openMenu === row.key + ':field'" @click.outside="openMenu = ''">
-															<template x-for="grp in fieldGroups" :key="grp.group">
+															<div class="fb-menu-filter-wrap">
+																<input type="text" class="fb-menu-filter" placeholder="Filter fields…" x-model="fieldFilter" @keydown.enter.prevent @click.stop/>
+															</div>
+															<template x-for="grp in visibleFieldGroups" :key="grp.group">
 																<div>
 																	<div class="fb-menu-group" x-text="grp.group"></div>
 																	<template x-for="f in grp.fields" :key="f.key">
@@ -207,6 +210,7 @@ templ BookShelf(
 																	</template>
 																</div>
 															</template>
+															<div class="fb-menu-empty" x-show="visibleFieldGroups.length === 0">No matching fields</div>
 														</div>
 													</div>
 													<!-- operator picker (negation lives here) -->