feat(Alert): Update design to match new design vision

mentioned in commit 9214d9c9

mentioned in merge request gitlab-org/editor-extensions/gitlab-jetbrains-plugin!884 (merged)

mentioned in merge request status-page!903

mentioned in merge request gitlab!164171 (merged)

mentioned in merge request gitlab!164330 (merged)

mentioned in merge request gitlab-org/frontend/playground/accessibility-scanner!49 (merged)

mentioned in merge request gitlab-org/frontend/pajamas-adoption-scanner!343 (merged)

mentioned in merge request gitlab-org/gitlab-services/design.gitlab.com!4026 (merged)

mentioned in merge request gitlab-org/gitlab-services/design.gitlab.com!4027 (merged)

mentioned in merge request gitlab!165126 (closed)