Support profile switching for EKS tools

### Describe the feature (Security related? please follow to report them to AWS Security directly.)

This tool is cited in AWS's documentation as the preferred method for connecting to the eks-mcp service, yet it does not currently support profile switching.

### Use Case

I need this feature because my team supports many eks clusters across many accounts and we would like to be able to configure one mcp proxy for this instead of having a one-to-one ratio.

### Proposed Solution

After examining the code, it appears that all that is needed for this to work is to add the EKS tools to the list of tools that need the profile switching middleware.

### Other Information

_No response_

### Acknowledgements

- [x] I may be able to implement this feature request
- [ ] This feature might incur a breaking change

Locate the profile-switching middleware configuration and the list of tools it covers, then identify the EKS tools that are currently omitted. Done means the EKS tools use profile switching so one proxy can serve clusters across multiple accounts.

Written by the indexing model from the issue text.