Improve code suggestion admin check

In scope of #458164 (closed) was added a simple check which is done automatically whenever user opens "Admin->Gitlab Duo Pro" page.

This check could be improved further to use .gl-card instead of flash alert and "retry" button as suggested in #458164 (comment 1943651205).

Update [2024-07-04]

We are evaluating a new holistic solution for this check and other checks related to Duo/AI features/Cloud Connectors. See #466698 (comment 1974006803).

Update [2024-07-15]

Closing this issue because the improvement to the Admin UI would be minor. Per #466698 (comment 1999597997), there is a separate issue #472477 (closed) to address AI-related checks in a holistic solution.