feat: support new authentication for code suggestions

Tomas Vik (OOO back on 2026-01-05)requested to merge
140-introduce-api-request-command into main

This MR connects the CodeSuggestionCompletionProvider to the new authentication introduced in gitlab-org/modelops/applied-ml/code-suggestions/ai-assist#56 (closed) and gitlab#404427 (closed)

web-ide-code-suggestion-auth

Related to #140 (closed)

Edited by Tomas Vik (OOO back on 2026-01-05)

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