Fix file tree refresh after convert and compiler sync on set-as-main

- Convert: backend now returns parentFolderId+isNew; frontend calls
  dispatchCreateDoc directly so the new file appears without a page refresh
- Set as main: infer compiler from file extension and POST both rootDocId
  and compiler together; updateProject propagates the change to the
  editor settings dropdown and project list immediately

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

services/web/frontend/js/features/ide-react/hooks/use-convert-doc.ts

@@ -1,5 +1,6 @@
 import { postJSON } from '@/infrastructure/fetch-json'
 import { useProjectContext } from '@/shared/context/project-context'
+import { useFileTreeData } from '@/shared/context/file-tree-data-context'
 import { useCallback, useState } from 'react'
 import {
   showExportDocumentError,
@@ -12,6 +13,7 @@ export default function useConvertDoc(
   docId: string | null
 ) {
   const { projectId } = useProjectContext()
+  const { dispatchCreateDoc } = useFileTreeData()
   const [converting, setConverting] = useState(false)
 
   const convert = useCallback(async () => {
@@ -19,17 +21,24 @@ export default function useConvertDoc(
     setConverting(true)
     hideExportDocumentError()
     try {
-      await postJSON(`/project/${projectId}/doc/${docId}/convert/${type}`, {
-        body: {},
-      })
+      const result = await postJSON(
+        `/project/${projectId}/doc/${docId}/convert/${type}`,
+        { body: {} }
+      )
       showExportDocumentSuccess(type)
+      if (result.isNew) {
+        dispatchCreateDoc(result.parentFolderId, {
+          _id: result.docId,
+          name: result.name,
+        })
+      }
     } catch (err: any) {
       const errorMessage = err?.data?.error
       showExportDocumentError(errorMessage)
     } finally {
       setConverting(false)
     }
-  }, [projectId, docId, type])
+  }, [projectId, docId, type, dispatchCreateDoc])
 
   return { convert, converting }
 }