/task handler re-encodes valid task kinds as a tuple with a type: ignore instead of TaskManager validating TaskKind #33

Location: src/perplexity_agent/tui/app.py:296, 305

The /task handler spells the valid kinds as the literal tuple ("search", "fetch") and silences the resulting mismatch with # type: ignore[arg-type], while TaskManager.add does no validation of its TaskKind.

Cost: the kind set is independently spelled in tasks.py's TaskKind Literal, _probe's branch, the app tuple, the usage string, and _HELP — adding a third kind (e.g. research) requires synchronized edits in 5 places, and the type: ignore hides any drift until a confusing runtime usage error.

Suggested fix: have TaskManager.add validate against a single source of truth (e.g. typing.get_args(TaskKind)) and derive the TUI's tuple/usage text from it; drop the ignore.

Found by /code-review (high effort).