fix(GlAlert): Migrate dismiss button to GlButton

• Integration MR: gitlab!57542 (merged)

What does this MR do?

• Migrates the dismiss button to GlButton.
• Adds styles to target the GlButton so that this doesn’t impact HAML and Ruby instances yet to be migrated.

Before	After

Does this MR meet the acceptance criteria?

Conformity

• Code review guidelines.
• GitLab UI's contributing guidlines.
• If it changes a Pajamas-compliant component's look & feel, the MR has been reviewed by a UX designer.
• If it changes GitLab UI's documentation guidelines, the MR has been reviewed by a Technical Writer.
• If the MR changes a component's API, integration MR(s) have been opened in the following projects to ensure that the @gitlab/ui package can be upgraded quickly after the changes are released:
  • GitLab: gitlab!57542 (merged)
  • CustomersDot: mr_url
  • Status Page: mr_url
• Added the ~"component:*" label(s) if applicable.

Security

N/A

Accessibility

If this MR adds or modifies a component, take a few moments to review the following:

• All actions and functionality can be done with a keyboard.
• Links, buttons, and controls have a visible focus state.
• All content is presented in text or with a text equivalent. For example, alt text for SVG, or aria-label for icons that have meaning or perform actions.
• Changes in a component’s state are announced by a screen reader. For example, changing aria-expanded="false" to aria-expanded="true" when an accordion is expanded.
• Color combinations have sufficient contrast.

Closes #1347 (closed), #1228 (closed)