refactor: clean up internal/api dead code and migrate to response builders

[javi11]

Summary

• Remove unused dead code from errors.go: ErrMsg* constants, APIErrorResponse type, NewAPIError, and NewAPIErrorResponse
• Delete responses_http.go entirely (5 legacy net/http response helpers never called anywhere)
• Remove legacy net/http parser functions (ParsePagination, ParseTimeParam) from parsers.go
• Migrate all inline c.JSON(fiber.Map{...}) responses in health_library_sync_handlers.go and rclone_handlers.go to established Respond* builder pattern

Test plan

• go build ./... passes
• go vet ./internal/api/... passes
• go test ./internal/api/... passes
• Verify library sync endpoints return correct response format (start, cancel, status, dry-run, needed)
• Verify rclone endpoints return correct response format (mount status, start, stop, test config, test connection, clear cache)

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