Quality of Service (QoS) in MQTT is well explained by the HiveMQ Team. With the exception of one subtle detail: QoS messages are never “upgraded”, so if the original publisher sent a message with QoS 0, a QoS 2 subscriber will still receive the message as QoS 0. That’s what Dominik from the HiveMQ Team explained in a comment and it was also reiterated by his colleague Dasha in another comment.

This applies for regular messages, as well as for the Last Will and Testament (LWT).

Another discussion about this explains the same thing but points to an interesting feature of the Mosquitto MQTT broker:

upgrade_outgoing_qos [ true | false ]

The MQTT specification requires that the QoS of a message delivered to a subscriber is never upgraded to match the QoS of the subscription.

Enabling this option changes this behavior. If "upgrade_outgoing_qos" is set "true", messages sent to a subscriber will always match the QoS of its subscription. This is a non-standard option not provided for by the spec.

Defaults to "false".