Fix JsonSafeParse violations in MCP ApiService

Doby Baxterrequested to merge
gitlab-community/gitlab-org/gitlab:mcp-json-safe-parse-clean into master

This MR supersedes !222565 (closed).

The previous branch had fallen significantly behind master, so I recreated the change on top of the latest master to avoid rebase conflicts and history drift.

The functional change remains the same:

  • Replace Gitlab::Json.parse with Gitlab::Json.safe_parse
  • Extend the rescue clause to handle Gitlab::Json::ParserError

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