claude-code-base-action tags are not synced, leading to failure due to outdated version of claude code

There is a separate mirror repo here https://github.com/anthropics/claude-code-base-action which used to be synced with the base-action in this repo. However, the syncing stopped in August of last year with `anthropics/claude-code-base-action@beta`. This version is hardcoded to use claude-code `1.0.88`, which now fails:

```
It looks like your version of Claude Code (1.0.88) needs an update.
A newer version (2.0.0 or higher) is required to continue.
```

I suggest that either:

1. https://github.com/anthropics/claude-code-base-action is archived, with a deprecation notice added.
2. there is a `v1` release of the base action, and this tracks the main action (ensuring always using the latest claude code)

I believe I originally had a use case for using the base action, but it looks like the main action is sufficiently customizable, which supports (1) above.