[Hackathon] fix(doctor): use the shared parseRequestTimeoutFlag — local copy's message has drifted #364

$ testsprite doctor --request-timeout abc
Error: Invalid request.
Flag `--request-timeout` is invalid: must be a positive number of seconds (got "abc").

$ testsprite project list --dry-run --request-timeout abc
Error: Invalid request.
Flag `--request-timeout` is invalid: "abc" is not valid — must be a positive number of seconds.

$ testsprite auth status --request-timeout abc
Error: Invalid request.
Flag `--request-timeout` is invalid: "abc" is not valid — must be a positive number of seconds.
Same flag, same bad input — two different messages depending on the command.
Expected
doctor produces the same validation error as every other command, from
the single shared implementation, so the wording (and any future behaviour
change) cannot drift per command again.
Actual
doctor resolves its common options through its own local
parseRequestTimeoutFlag copy instead of importing the shared one from
src/lib/client-factory.ts, and the copy's message wording differs.
Suggested fix
Delete the local copy in src/commands/doctor.ts and import
parseRequestTimeoutFlag from ../lib/client-factory.js, like the other
commands do. Align any doctor tests that reference the old wording.
No behaviour change beyond the message text: both copies reject the same
inputs with exit 5 today.
Environment
CLI version: 0.14.0 (built from source at 988c035)
Node: v24.20.0
OS: Linux x86_64


### Confirmations

- [x] I have searched existing issues and this is not a duplicate.
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