feat: Use new compose conversation in conversation sidebar (#11085)

# Pull Request Template

## Description

This PR includes the implementation of the new Compose Conversation form
in the conversation sidebar, replacing the old one.

## Type of change

- [x] New feature (non-breaking change which adds functionality)

## How Has This Been Tested?

### Loom video

https://www.loom.com/share/4312e20a63714eb892d7b5cd0dcda893?sid=9bd5254e-2b1f-462c-b2c1-a3048a111683

## Checklist:

- [x] My code follows the style guidelines of this project
- [x] I have performed a self-review of my code
- [x] I have commented on my code, particularly in hard-to-understand
areas
- [ ] I have made corresponding changes to the documentation
- [x] My changes generate no new warnings
- [ ] I have added tests that prove my fix is effective or that my
feature works
- [x] New and existing unit tests pass locally with my changes
- [ ] Any dependent changes have been merged and published in downstream
modules

app/javascript/dashboard/components/widgets/InboxDropdownItem.vue

@@ -1,76 +0,0 @@
-<script>
-import {
-  getInboxClassByType,
-  getReadableInboxByType,
-} from 'dashboard/helper/inbox';
-
-export default {
-  components: {},
-  props: {
-    name: {
-      type: String,
-      default: '',
-    },
-    inboxIdentifier: {
-      type: String,
-      default: '',
-    },
-    channelType: {
-      type: String,
-      default: '',
-    },
-  },
-  computed: {
-    computedInboxIcon() {
-      if (!this.channelType) return 'chat';
-      const classByType = getInboxClassByType(
-        this.channelType,
-        this.inboxIdentifier
-      );
-      return classByType;
-    },
-    computedInboxType() {
-      if (!this.channelType) return 'chat';
-      const classByType = getReadableInboxByType(
-        this.channelType,
-        this.inboxIdentifier
-      );
-      return classByType;
-    },
-  },
-};
-</script>
-
-<template>
-  <div class="flex items-center h-[2.375rem] min-w-0 py-0 px-1">
-    <span
-      class="inline-flex rounded mr-1 rtl:ml-1 rtl:mr-0 bg-slate-25 dark:bg-slate-700 p-0.5 items-center flex-shrink-0 justify-center w-6 h-6"
-    >
-      <fluent-icon
-        :icon="computedInboxIcon"
-        size="14"
-        class="text-slate-800 dark:text-slate-200"
-      />
-    </span>
-    <div class="flex flex-col w-full min-w-0 ml-1 mr-1">
-      <h5 class="option__title">
-        {{ name }}
-      </h5>
-      <p
-        class="option__body overflow-hidden whitespace-nowrap text-ellipsis"
-        :title="inboxIdentifier"
-      >
-        {{ inboxIdentifier || computedInboxType }}
-      </p>
-    </div>
-  </div>
-</template>
-
-<style lang="scss" scoped>
-.option__body {
-  @apply inline-block text-slate-600 dark:text-slate-200 leading-[1.3] min-w-0 m-0;
-}
-.option__title {
-  @apply leading-[1.1] text-xs m-0 text-slate-800 dark:text-slate-100;
-}
-</style>