[15 Feb+] Remove proxy-through-com logic for CS

What does this MR do and why?

We have a logic that revolves around proxying Code Suggestions requests through .com from SM, like that: https://gitlab.com/gitlab-org/gitlab/-/blob/2856b5104a7d3974768111311d045f1930e7c2a5/ee/lib/api/code_suggestions.rb#L58
That's how we initially implemented "Cloud Connected" Code Suggestions, but switched to a different implementation starting GL 16.3.

Starting from the Code Suggestions free access cut-off date (Feb 15th), it stops working because Code Suggestions will only work for GitLab with seat assignments (later versions).

In this MR, we remove this logic and simplify the code.

⛳ This MR also cleans up the code_suggestions_for_instance_admin_enabled feature flag. All FF references are removed, so CI enforces the FF definition removal in the same MR.
Related FF issue: https://gitlab.com/gitlab-org/gitlab/-/issues/438255

MR acceptance checklist

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How to set up and validate locally

This should be no-op for GitLab SM.
It's enough to test that Code Suggestions still work locally as usual.

Related to #439587