I never tested as well, but I think having SAML and Always ON feature together fits your customer's use-case.
You can have the AnyConnect client vpn software configured with a custom profile where the Always ON feature is enabled. You can read more about it here.
I would also Make sure that MX option Session Timeout is "None" ; doing this would allow a remote user to stay connected regardless of network activity over the tunnel and also reconnect when laptop resumes from sleep state.
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