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-next/NewConversation/components/InboxSelector.vue

@@ -52,7 +52,7 @@ const targetInboxLabel = computed(() => {
     </label>
     <div
       v-if="targetInbox"
-      class="flex items-center gap-1.5 rounded-md bg-n-alpha-2 truncate px-3 h-7 min-w-0"
+      class="flex items-center gap-1.5 rounded-md bg-n-alpha-2 truncate ltr:pl-3 rtl:pr-3 ltr:pr-1 rtl:pl-1 h-7 min-w-0"
     >
       <span class="text-sm truncate text-n-slate-12">
         {{ targetInboxLabel }}