Support reporting all check failures without stopping after formatting errors #3366

Description

Currently, vp check stops when formatting issues are found, so lint and type errors are not reported until the formatting issues are resolved.

This requires multiple runs to discover all problems in a project. Running vp check --fix can fix formatting and some lint issues, but it modifies files and cannot fix every lint or type error.

It would be useful to report all enabled check results in a single run without modifying files.

With this flag:

• Run all enabled checks even if formatting issues are found.
• Report formatting, lint, and type errors in the same invocation.
• Return a non-zero exit code if any enabled check fails.
• Respect existing options such as --no-fmt, --no-lint, and --deny-warnings.
• Preserve the current fail-fast behavior when the flag is omitted.
  Type checking would still depend on the existing project configuration.

Suggested solution

Add an opt-in flag such as:

vp check --keep-going

Alternative

Run formatting and lint checks separately, or fix formatting issues before running vp check again.

Additional context

No response

Validations

• Read the Contributing Guidelines.
• Confirm this request is for Vite+ itself and not for Vite, Vitest, tsdown, Rolldown, or Oxc.
• Check that there isn't already an issue requesting the same feature.