Investigate disappearing directory issue during expression compiler initialization.

We encounter an intermittent failure during debugging applications in google3:

```
[SEVERE] ExpressionCompilerService: Starting...
Unhandled exception:
FileSystemException: Getting current working directory failed, path = '' (OS Error: No such file or directory, errno = 2)
#0 _Directory.current (dart:io/directory_impl.dart:42:7)
#1 Directory.current (dart:io/directory.dart:136:25)
#2 _Compiler.start (package:dwds/src/services/expression_compiler_service.dart:112:45)
#3 ExpressionCompilerService.initialize (package:dwds/src/services/expression_compiler_service.dart:303:36)

#4 ChromeProxyService.updateCompilerDependencies (package:dwds/src/services/chrome_proxy_service.dart:180:7)

```

See the PR mentioned below for description and a repro (reverting the change and trying to debug an ACX demo will reproduce the problem almost every time).

We should create a smaller repro and find and fix the underlying problem.

Reproduce the failure while debugging the ACX demo, then inspect _Compiler.start in package/dwds/src/services/expression_compiler_service.dart and its callers in ExpressionCompilerService.initialize and ChromeProxyService.updateCompilerDependencies. Create the smaller reproduction requested and identify the cause of the missing current working directory; done means the repro no longer fails during compiler initialization.

Written by the indexing model from the issue text.