feat: record and expose terminal upstream interception errors (#26961)

Categorises the terminal error of a failed interception and persists it
on the interception record, then surfaces it on the AI Gateway API.

- Categorise into an enum (`bad_request`, `unauthorized`,
  `rate_limited`, `overloaded`, `server_error`, `unknown`), unwrapping
  the ResponseError envelope, the upstream Anthropic/OpenAI SDK errors,
  and key-pool exhaustion so blocking and streaming paths agree.
- Thread the type and raw message through the recorder dRPC into the
  `aibridge_interceptions` row (optional proto fields; NULL on success).
- Expose the error on the AI Gateway thread API from the root
  interception.

*This PR was produced by opencode (agent) using the `anthropic/claude-opus-4-8` model, under human direction and review.*

coderd/database/dbgen/dbgen.go

@@ -2022,6 +2022,8 @@ func AIBridgeInterception(t testing.TB, db database.Store, seed database.InsertA
 			ID:             interception.ID,
 			EndedAt:        *endedAt,
 			CredentialHint: takeFirst(seed.CredentialHint, ""),
+			ErrorType:      database.NullAIBridgeInterceptionErrorType{},
+			ErrorMessage:   sql.NullString{},
 		})
 		require.NoError(t, err, "insert aibridge interception")
 	}