Profiler file not written during watch mode

[Eazash]

Which packages are impacted by your issue?

@graphql-codegen/cli

Describe the bug

When trying to debug performance issues with the watch mode, I noticed that the generator doesn't output a profile file. This only happens during watch mode, as regular codegen generates the file

Your Example Website or App

https://codesandbox.io/p/devbox/interesting-architecture-xtt6xd

Steps to Reproduce the Bug or Issue

1. Run graphql-codegen --config ./codegen.ts --watch --profile
2. Make changes to your documents
3. Stop the watcher with Ctrl + C
4. Observe that there is no codegen-[timestamp].json present

Expected behavior

I expect a codegen-[timestamp].json to be present

Screenshots or Videos

No response

Platform

• OS: macOS
• NodeJS: v20.12.1
• @graphql-codegen/cli: ^5.0.6
• @graphql-codegen/typescript: ^4.1.6
• @graphql-codegen/typescript-operations: ^4.6.1
• graphql: ^16.2.0

Codegen Config File

No response

Additional context

No response