Frontend/Backend: Update UI to show variables

Summary

This issue is related to the discussion in step 3 of #362262 (closed) where we want to update the UI to expose the variables used, rather than relying on the name. This may require updating the API to contain the information if not already available.

Proposal

Add UI elements to expose the variables used, rather than relying on the name. This may require updating the API to contain the information if not already available. For anyone picking up the issue, confirmation is needed to determine whether variables are already available in the API (which would make this frontend only) or not (backend work would be additionally needed here)

Additional details

Some relevant technical details, if applicable, such as:

• Does this need a feature flag?
• Does there need to be an associated instrumentation issue created related to this work?
• Is there an example response showing the data structure that should be returned (new endpoints only)?
• What permissions should be used?
• Is this EE or CE?
  • EE
  • CE
• Additional comments:

Implementation Table

Group	Issue Link
backend	Backend: No pipelines created when matrix var i... (#362262 - closed)
backend	Backend: Match Ci::BuildNeed name limit with jo... (#420669 - closed)
backend / frontend	👈 You are here
backend	Backend: Allow Custom Matrix Names (#428169 - closed)

Links/References