[Bug] PubMed MCP server returns "Rate exceeded" error on basic search requests

### Description

The PubMed MCP server installed via the life-sciences marketplace consistently returns a "Rate exceeded" error when attempting basic search queries through Claude Desktop (Cowork mode). The error occurs on the very first request of a session, suggesting this is not caused by actual excessive usage.

### Steps to Reproduce

1. Install the PubMed MCP via the bio-research plugin (life-sciences marketplace)
2. Start a new Cowork session in Claude Desktop
3. Attempt any `search_articles` call (e.g., query: "CRISPR gene editing", max_results: 3)

### Expected Behavior

The search should return PubMed article results.

### Actual Behavior

The server returns a "Rate exceeded" error immediately, even on the first request of a new session.

### Workaround

Using a third-party PubMed MCP server (e.g., [Augmented-Nature/PubMed-MCP-Server](https://github.com/Augmented-Nature/PubMed-MCP-Server)) as a substitute works without issues.

### Environment

- **Product**: Claude Desktop (Cowork mode, research preview)
- **Plugin**: bio-research (life-sciences marketplace)
- **MCP server**: PubMed (`anthropics/healthcare/pubmed`)
- **Date observed**: February 2026

### Additional Context

- All other bio-research plugin skills (single-cell RNA QC, scvi-tools, Nextflow, etc.) work fine — only the PubMed MCP is affected.
- The unofficial PubMed MCP (`search_pubmed`, `get_paper_fulltext`) connected in the same session works without rate limit issues, confirming the problem is specific to the official PubMed MCP server.
- No existing issues found in this repo or `anthropics/claude-code` regarding this specific problem.