fix(cache): disable setup-bun cache to avoid 5-retry HTML-error burn

[MukundaKatta]

Why

Closes #1252.

anthropics/claude-code-action@v1's post-job cache save fails consistently on every second-and-subsequent run against the same PR ref. From the issue:

Attempt 1 of 5 failed with error: Unexpected token '<', "<!DOCTYPE "... is not valid JSON. Retrying request in 3000 ms...
Attempt 2 of 5 failed with error: Unexpected token '<', "<!DOCTYPE "... is not valid JSON. Retrying request in 5276 ms...
...
Warning: Failed to save: Failed to FinalizeCacheEntryUpload: Failed to make request after 5 attempts

Root cause: oven-sh/setup-bun@v2.2.0's post step calls @actions/cache.saveCache with a deterministic key derived from the Bun download URL (bun-<hash>). The key is identical across runs, so on every PR re-push the GitHub cache API rejects the duplicate key+ref with a 409 (HTML body). @actions/cache@5.x treats the unparsable response as transient and burns ~20-30s on 5 retries before surfacing a warning. The cache key isn't ref-aware and setup-bun doesn't expose a way to override it, so the issue is unavoidable as long as the cache is enabled.

This burns ~20-30s of wallclock per PR push after the first, plus persistent warning noise that masks real cache issues. See #1252 for the full repro and cache-entry inspection.

What

Pass no-cache: true to oven-sh/setup-bun in both action.yml and base-action/action.yml. The 35 MB Bun binary downloads from bun.sh in 2-3s on GitHub-hosted runners (curl install also relies on this in PR #819), so disabling the cache is a net wallclock win and removes the warning entirely.

This is the smallest action-side fix — alternatives would require either patching setup-bun upstream (issue author's option 2) or replacing it with curl-based install (issue author's option 4 / open PR #819, which targets a separate GHES bug).

Tested

Manual verification only — the change is YAML-only inside the composite step, and there are no unit tests for action.yml in test/ (tests cover TypeScript logic).

To verify after merge, run the action twice on the same PR ref and confirm:

• The "Attempt 1 of 5 failed" warning no longer appears in the post-step.
• The Install Bun step prints Downloading a new version of Bun on every run instead of Using a cached version of Bun.
• Total Install Bun step time stays within a few seconds.