[clsi] prepare for clsi-cache survey (#29274)

* [clsi] add stats and timings to compile response from clsi-cache

* [clsi] set downloadedFromCache when previously downloaded for synctex

Assumption: every compile will emit an output.log. When the output.log
is missing, but the output.synctex.gz exists, it must have been
downloaded from the cache.
GitOrigin-RevId: 41ea34880931e3c43dda3bc9eb26c0d02054894d

services/clsi/app/js/CompileManager.js

@@ -561,6 +561,13 @@ async function _runSynctex(projectId, userId, command, opts) {
       let downloadedFromCache = false
       try {
         await _checkFileExists(directory, 'output.synctex.gz')
+        if (compileFromClsiCache) {
+          try {
+            await _checkFileExists(directory, 'output.log')
+          } catch (err) {
+            if (err instanceof Errors.NotFoundError) downloadedFromCache = true
+          }
+        }
       } catch (err) {
         if (
           err instanceof Errors.NotFoundError &&