collect-inputs.ts input map has drifted from action.yml: 11 removed inputs tracked, 19 current inputs missing (including prompt)

## Summary

The input map in [`src/entrypoints/collect-inputs.ts`](https://github.com/anthropics/claude-code-action/blob/d721746d683d812e669ce117cebe55a85fbd9c3e/src/entrypoints/collect-inputs.ts#L2-L34) has drifted out of sync with the inputs actually declared in `action.yml`. It currently tracks **11 inputs that no longer exist** and **omits 19 that do**, including `prompt` — the input that determines whether the action runs in tag mode or agent mode.

Because this function's output becomes the `GITHUB_ACTION_INPUTS` environment variable ([`base-action/src/parse-sdk-options.ts#L280-L282`](https://github.com/anthropics/claude-code-action/blob/d721746d683d812e669ce117cebe55a85fbd9c3e/base-action/src/parse-sdk-options.ts#L280-L282)), the usage signal it produces is currently incomplete and partly meaningless.

## Reproduction

Diffing the declared inputs in `action.yml` against the keys in `inputDefaults`:

```console
$ awk '/^inputs:/,/^outputs:/' action.yml | grep -E "^ [a-z_]+:" | tr -d ' :' | sort > declared.txt
$ grep -oE '^ [a-z_]+:' src/entrypoints/collect-inputs.ts | tr -d ' :' | sort > collected.txt

$ comm -13 declared.txt collected.txt # tracked but no longer declared
allowed_tools
anthropic_model
claude_env
custom_instructions
direct_prompt
disallowed_tools
fallback_model
max_turns
mode
model
override_prompt

$ comm -23 declared.txt collected.txt # declared but not tracked
allowed_non_write_users
bot_id
bot_name
branch_name_template
claude_args
display_report
exclude_comments_by_actor
include_comments_by_actor
include_fix_links
path_to_bun_executable
path_to_claude_code_executable
plugin_marketplaces
plugins
prompt
show_full_output
track_progress
use_bedrock
use_foundry
use_vertex
```

All 11 stale entries are v0.x inputs removed in the v1.0 migration — they are listed as deprecated in `docs/usage.md` and `docs/configuration.md`.

## Impact

`collectActionInputsPresence()` reports, for each input, whether the user set it to something other than its default. The current map means that signal cannot observe:

- **`prompt`** — the single input that selects agent mode over tag mode (`src/modes/detector.ts`). Presence of a prompt is arguably the most significant thing about any given invocation, and it is not tracked.
- **`claude_args`** — the primary v1.0 configuration surface, which replaced `allowed_tools`, `disallowed_tools`, `max_turns`, `model`, and `fallback_model`. All five predecessors are still tracked; their replacement is not.
- **`use_bedrock` / `use_vertex` / `use_foundry`** — which cloud provider the run targets.
- **`track_progress`**, **`plugins`**, **`plugin_marketplaces`**, **`allowed_non_write_users`** — all newer features.

Meanwhile the 11 stale keys can never be anything but `false`, since `ALL_INPUTS` (populated from `toJson(inputs)` at `action.yml#L317`) will never contain a key that `action.yml` does not declare. They are pure noise in the output.

## Related: `inputs.mode` is referenced but never declared

Same root cause. [`action.yml#L290`](https://github.com/anthropics/claude-code-action/blob/d721746d683d812e669ce117cebe55a85fbd9c3e/action.yml#L290) sets:

```yaml
MODE: ${{ inputs.mode }}
```

but there is no `mode:` entry in the `inputs:` block — it was removed when mode detection became automatic. The expression resolves to the empty string, and nothing in `src/` reads `process.env.MODE`. It should be deleted along with the stale map entries.

## Why this keeps happening

There is no mechanism tying the two lists together, so any input added to or removed from `action.yml` silently diverges from `collect-inputs.ts`. The drift above accumulated across the whole v1.0 migration without surfacing.

## Suggested fix

1. Regenerate `inputDefaults` from the current `action.yml`, dropping the 11 stale keys and adding the 19 missing ones with their declared defaults.
2. Remove the `MODE` env line from `action.yml`.
3. Add a drift-guard test that parses `action.yml` and asserts the key sets match exactly, so this cannot silently recur. [`test/action-metadata.test.ts`](https://github.com/anthropics/claude-code-action/blob/d721746d683d812e669ce117cebe55a85fbd9c3e/test/action-metadata.test.ts) is the natural home — it already reads and asserts against `action.yml`, and currently contains a single test.

A question for maintainers before I open a PR: should the guard assert exact set equality, or should there be an explicit opt-out list for inputs deliberately excluded from the presence signal (secrets such as `anthropic_api_key` and `github_token` are currently tracked, so I assume exact equality is intended — but I'd rather confirm than guess).

Happy to submit the fix and the guard test together.

## Environment

- Repository at `d721746d683d812e669ce117cebe55a85fbd9c3e` (`main`)