[web] add clsi-cache prompts (#29281)

* [web] add clsi-cache prompts

* [web] add new editor variant to segmentation

* [web] add tests for useNewEditorVariant

* [web] adjust start of using clsi-cache in split-test

GitOrigin-RevId: c9c5b1eff2ceefb65ef82516d9074cb971cb4c48

services/web/types/compile.ts

@@ -1,3 +1,5 @@
+import { ClsiCachePromptVariant } from '@/features/pdf-preview/util/types'
+
 export type Chunk = {
   start: number
   end: number
@@ -69,9 +71,10 @@ export type CompileResponseData = {
   pdfDownloadDomain?: string
   pdfCachingMinChunkSize: number
   validationProblems: any
-  stats: any
-  timings: any
+  stats?: Record<string, number>
+  timings?: Record<string, number>
   outputFilesArchive?: CompileOutputFile
+  clsiCachePromptVariant?: ClsiCachePromptVariant
 
   // assigned on response body by DocumentCompiler in frontend
   rootDocId?: string | null