Updates styling for buttons in the editor

[vraja-pro]

Context

• We want to match update the buttons in our editor to use ui library.

Summary

This PR can be summarized in the following changelog entry:

• Updates style for the AI buttons.

Relevant technical choices:

• Changes the design of buttons in the editor.

Test instructions

Test instructions for the acceptance test before the PR gets merged

This PR can be acceptance tested by following these steps:

• Edit a post and check the replacement variables button matches the design.
• Edit a draft post and check the pre publish buttons match the design.
• Follow the test instruction here to see the Generate buttons in the pre publish sidebar.

Relevant test scenarios

• Changes should be tested with the browser console open
• Changes should be tested on different posts/pages/taxonomies/custom post types/custom taxonomies
• Changes should be tested on different editors (Default Block/Gutenberg/Classic/Elementor/other)
• Changes should be tested on different browsers
• Changes should be tested on multisite

Test instructions for QA when the code is in the RC

• QA should use the same steps as above.

QA can test this PR by following these steps:

Impact check

This PR affects the following parts of the plugin, which may require extra testing:

Other environments

• This PR also affects Shopify. I have added a changelog entry starting with [shopify-seo], added test instructions for Shopify and attached the Shopify label to this PR.

Documentation

• I have written documentation for this change. For example, comments in the Relevant technical choices, comments in the code, documentation on Confluence / shared Google Drive / Yoast developer portal, or other.

Quality assurance

• I have tested this code to the best of my abilities.
• During testing, I had activated all plugins that Yoast SEO provides integrations for.
• I have added unit tests to verify the code works as intended.
• If any part of the code is behind a feature flag, my test instructions also cover cases where the feature flag is switched off.
• I have written this PR in accordance with my team's definition of done.
• I have checked that the base branch is correctly set.

Innovation

• No innovation project is applicable for this PR.
• This PR falls under an innovation project. I have attached the innovation label.
• I have added my hours to the WBSO document.

Fixes https://github.com/Yoast/ux/issues/313