omo-ai beta migration can select a cached or higher-priority legacy omo

## Summary

Users installing the senpi-based `omo-ai@beta` can still execute a cached legacy `omo` wrapper in the same zsh session. The installation succeeds, but `omo` shows the legacy `oh-my-opencode` command help instead of launching the bundled senpi CLI.

Primary packaging issue: https://github.com/code-yeongyu/oh-my-openagent/issues/6686

## Reproduction

1. Have `~/.local/bin/omo` from legacy OMO and invoke it once in zsh.
2. Keep the npm global bin directory earlier in PATH.
3. Run `npm i -g omo-ai@beta`.
4. Run `omo` in the same zsh session.

Observed:

```text
cached=/Users/jgp/.local/bin/omo
omo --version => 4.19.4
Usage: oh-my-opencode [options] [command]
```

After `rehash`:

```text
omo --version => 2026.8.9-2
```

The latter is the expected bundled `@code-yeongyu/senpi` version, confirming that the senpi package itself is installed and runnable.

## Impact

Migration users may conclude that senpi/omo-ai was not installed, reinstall repeatedly, or report a false binary/package conflict. `which -a omo` can show the npm binary first while zsh still executes its cached path, making diagnosis non-obvious.

## Workaround

```sh
rehash
# or
hash -r
```

Opening a new shell also clears the stale command resolution.

## Requested coordination

Please keep this issue as the senpi-side consumer report and cross-reference the packaging fix in `code-yeongyu/oh-my-openagent`. The actionable launcher/install changes belong to that repository; no senpi core behavior change has been identified.

Environment: macOS Darwin 25.5.0 arm64, zsh, Node.js 24.14.0, `omo-ai@5.0.0-0.beta.3`. Internal tracking: LAB-39.

Start with the reproduction in this issue: invoke the legacy ~/.local/bin/omo, install omo-ai@beta, then run omo in the same zsh session and compare it after rehash. The requested launcher and install fix belongs to code-yeongyu/oh-my-openagent issue #6686; done means migration no longer resolves the cached legacy wrapper, while senpi core remains unchanged.

Written by the indexing model from the issue text.