Improve GlListbox search input

What does this MR do?

It creates a new component for the GlListbox search input according to the new designs and replaces the currently used GlSearchBoxByType with it. We could have used GlSearchBoxByType but it requires a lot of overwriting of the styles as well as updating the component to allow adjusting different search icon sizes. The new one is much cleaner and is specifically adjusted for the GlListbox and can be used later for other dropdowns.

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: mr_url
  • CustomersDot: mr_url
  • Status Page: mr_url
• Added the ~"component:*" label(s) if applicable.

Security

If this MR contains changes to processing or storing of credentials or tokens, authorization and authentication methods and other items described in the security review guidelines:

• Label as security and @ mention @gitlab-com/gl-security/appsec
• Security reports checked/validated by a reviewer from the AppSec team

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.

References #1874 (closed)