refactor(server): replace try/catch with neverthrow Result types

[kira-autonoma]

Closes #581

Summary

Replaces all try/catch blocks in packages/app/server with typed neverthrow Result and ResultAsync types, providing exhaustive, compile-time error handling throughout the server.

Changes

New: src/errors/results.ts

Discriminated union error types for each layer:

• DbError — database operation failures with structured context
• AuthError — authentication/authorization failures with subtypes
• SettleError — x402 payment settlement failure variants
• RefundError — refund transfer failures
• ResourceError — top-level handler errors composing the above

Refactored: handlers/settle.ts

• Returns ResultAsync<SettleSuccess, SettleError> instead of Promise<... | undefined>
• Uses fromThrowable to wrap the synchronous validateXPaymentHeader
• Full .andThen() chain: smart account → header parse → payload validate → amount check → facilitator settle
• Removed res: Response from signature — callers own the HTTP response

Refactored: handlers/refund.ts

• Returns ResultAsync<void, RefundError> instead of swallowing errors
• Callers decide how to handle refund failures (log, alert, etc.)

Refactored: resources/handler.ts

• handleApiRequest → ResultAsync<TOutput, ResourceError> via chained .andThen()
• executeResourceWithRefund → ResultAsync<TOutput, ResourceError>; refund on error via .mapErr()
• handle402Request → ResultAsync<TOutput, ResourceError> composing settle and executeResourceWithRefund
• handleResourceRequest uses .match() at the HTTP boundary — no try/catch
• handleResourceRequestWithErrorHandling wraps in ResultAsync.fromPromise and .match()

Refactored: services/DbService.ts

• validateApiKey → ResultAsync<ApiKeyValidationResult, AuthError>
• getBalance → ResultAsync<Balance, DbError>
• createPaidTransaction → ResultAsync<Transaction, DbError>
• createFreeTierTransaction → ResultAsync<{transaction, userSpendPoolUsage}, DbError>

Refactored: services/EchoControlService.ts + FreeTierService.ts

• verifyApiKey, getBalance, createTransaction, createFreeTierTransaction, createPaidTransaction all propagate ResultAsync
• Errors surfaced via .isErr() checks with typed error variants

Design Decisions

• fromThrowable wraps sync-throwing functions at the boundary; async operations use ResultAsync.fromPromise
• .match() at HTTP boundary — Results never leak into Express response handlers
• cause: unknown on external-facing error variants where the underlying throw type cannot be statically known
• Discriminated unions over class hierarchies — exhaustive switch on error.type is idiomatic neverthrow

TypeScript Status

Zero new type errors introduced. Pre-existing infrastructure errors (generated/prisma not generated, workspace SDK not built) are unaffected and unchanged.

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