feat: Migrate availability mixins to composable and helper (#11596)

# Pull Request Template

## Description

**This PR includes:**

* Refactored two legacy mixins (`availability.js`,
`nextAvailability.js`) into a Vue 3 composable (`useAvailability`),
helper module and component based rendering logic.
* Fixed an issue where the widget wouldn't load if business hours were
enabled but all days were unchecked.
* Fixed translation issue
[[#11280](https://github.com/chatwoot/chatwoot/issues/11280)](https://github.com/chatwoot/chatwoot/issues/11280).
* Reduced code complexity and size.
* Added test coverage for both the composable and helper functions.

## Type of change

- [x] Bug fix (non-breaking change which fixes an issue)

## How Has This Been Tested?

### Loom video

https://www.loom.com/share/2bc3ed694b4349419505e275d14d0b98?sid=22d585e4-0dc7-4242-bcb6-e3edc16e3aee

### Story
<img width="995" height="442" alt="image"
src="https://github.com/user-attachments/assets/d6340738-07db-41d5-86fa-a8ecf734cc70"
/>



## 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
- [x] 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


Fixes https://github.com/chatwoot/chatwoot/issues/12012

---------

Co-authored-by: Muhsin Keloth <muhsinkeramam@gmail.com>
Co-authored-by: Pranav <pranav@chatwoot.com>
Co-authored-by: Shivam Mishra <scm.mymail@gmail.com>

app/javascript/widget/views/Home.vue

@@ -1,7 +1,7 @@
 <script>
 import TeamAvailability from 'widget/components/TeamAvailability.vue';
 import { mapGetters } from 'vuex';
-import routerMixin from 'widget/mixins/routerMixin';
+import { useRouter } from 'vue-router';
 import configMixin from 'widget/mixins/configMixin';
 import ArticleContainer from '../components/pageComponents/Home/Article/ArticleContainer.vue';
 export default {
@@ -10,7 +10,11 @@ export default {
     ArticleContainer,
     TeamAvailability,
   },
-  mixins: [configMixin, routerMixin],
+  mixins: [configMixin],
+  setup() {
+    const router = useRouter();
+    return { router };
+  },
   computed: {
     ...mapGetters({
       availableAgents: 'agent/availableAgents',
@@ -21,9 +25,9 @@ export default {
   methods: {
     startConversation() {
       if (this.preChatFormEnabled && !this.conversationSize) {
-        return this.replaceRoute('prechat-form');
+        return this.router.replace({ name: 'prechat-form' });
       }
-      return this.replaceRoute('messages');
+      return this.router.replace({ name: 'messages' });
     },
   },
 };