…ent (#6047)

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## Background

Splits up #5972 into package changes
and updates to examples.

## Summary

Moves capabilities validation downstream to the request level instead of
the method level.

This PR adds a new private `assertCapability` method called at the
request level. This means our custom, lightweight client defaults strict
mode to true for tool listing and tool calling.

## Verification

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## Tasks

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- [x] Tests have been added / updated (for bug fixes / features)
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## Future Work

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## Related Issues

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