I’n Windows it is not stored in a keyring but instead in the registry. This has basically the same security threat model as a local key file.
The ssh-agent on Linux will do what you want with effectively the same security. The biggest difference being that it doesn’t run as a system service but instead runs in userspace which can make it easier to dump memory. There are some other agent services out there with additional security options but they don’t change the threat model much.