Verify canary release

• I verified that the issue exists in the latest Turborepo canary release.

Link to code that reproduces this issue

n/a

Which canary version will you have in your reproduction?

n/a

Enviroment information

$ turbo info
turbo 2.3.0

CLI:
   Version: 2.3.0
   Daemon status: Not running
   Package manager: pnpm9

Platform:
   Architecture: x86_64
   Operating system: windows
   WSL: false

Environment:
   CI: None
   Terminal (TERM): xterm-256color
   Terminal program (TERM_PROGRAM): unknown
   Terminal program version (TERM_PROGRAM_VERSION): unknown
   Shell (SHELL): C:\Program Files\Git\usr\bin\bash.exe
   stdin: false

Expected behavior

Following from a discussion on the original FR:
--output-logs=errors-only doesn't work for turbo watch (nor when "outputLogs": "errors-only" is configured for the task).

Actual behavior

WRT log verbosity, turbo watch behaves the same as turbo run.

To Reproduce

n.f.a

Additional context

No response