[Issue #39] Use latest @common-grants/core library

[widal001]

Summary

Updates the website/ and the examples/custom-api/ to use the latest version of the @common-grants/core library.

• Fixes [Spec] Create v0.1.0-alpha library #39
• Time to review: 2 minutes

Changes proposed

What was added, updated, or removed in this PR.

• Bumps the @common-grants/core version used by the website/ and examples/custom-api/ to the latest version.
• Updates the examples/custom-api/ to adopt the new library API

Context for reviewers

Testing instructions, background context, more in-depth details of the implementation, and anything else you'd like to call out or ask reviewers. Explain how the changes were verified.

1. Checkout the PR locally
2. Change directory into examples/custom-api/
3. Run npm run docs to preview the updated example
4. Change directory into website/
5. Run npm run dev to preview the updated website

Additional information

Screenshots, GIF demos, code examples or output to help show the changes working as expected.

Custom API example

Website docs

[widal001]

Closing because I need to cherry pick these changes onto the main branch