feat: Add search functionality for public portal (#5683)

Co-authored-by: Pranav Raj S <pranav@chatwoot.com>

app/javascript/portal/components/PublicSearchInput.vue

@@ -0,0 +1,60 @@
+<template>
+  <div
+    class="w-full flex items-center rounded-md border-solid  h-16 bg-white px-4 py-2 text-slate-600"
+    :class="{
+      'shadow border-2 border-woot-100': isFocused,
+      'border border-slate-50 shadow-sm': !isFocused,
+    }"
+  >
+    <fluent-icon icon="search" />
+    <input
+      :value="value"
+      type="text"
+      class="w-full search-input focus:outline-none text-base h-full bg-white px-2 py-2
+    text-slate-700 placeholder-slate-500 sm:text-sm"
+      :placeholder="searchPlaceholder"
+      role="search"
+      @input="onChange"
+      @focus="onFocus"
+      @blur="onBlur"
+    />
+  </div>
+</template>
+
+<script>
+import FluentIcon from 'shared/components/FluentIcon/Index.vue';
+
+export default {
+  components: {
+    FluentIcon,
+  },
+  props: {
+    value: {
+      type: [String, Number],
+      default: '',
+    },
+    searchPlaceholder: {
+      type: String,
+      default: '',
+    },
+  },
+  data() {
+    return {
+      isFocused: false,
+    };
+  },
+  methods: {
+    onChange(e) {
+      this.$emit('input', e.target.value);
+    },
+    onFocus(e) {
+      this.isFocused = true;
+      this.$emit('focus', e.target.value);
+    },
+    onBlur(e) {
+      this.isFocused = false;
+      this.$emit('blur', e.target.value);
+    },
+  },
+};
+</script>