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/ContactSelector.vue

@@ -113,7 +113,8 @@ const handleInput = value => {
       </div>
       <div
         v-else-if="selectedContact"
-        class="flex items-center gap-1.5 rounded-md bg-n-alpha-2 px-3 min-h-7 min-w-0"
+        class="flex items-center gap-1.5 rounded-md bg-n-alpha-2 min-h-7 min-w-0"
+        :class="!contactId ? 'ltr:pl-3 rtl:pr-3 ltr:pr-1 rtl:pl-1' : 'px-3'"
       >
         <span class="text-sm truncate text-n-slate-12">
           {{
@@ -123,6 +124,7 @@ const handleInput = value => {
           }}
         </span>
         <Button
+          v-if="!contactId"
           variant="ghost"
           icon="i-lucide-x"
           color="slate"