MQTT 3 defines a couple of parameters that can be considered as Connection Properties:

http://docs.oasis-open.org/mqtt/mqtt/v3.1.1/os/mqtt-v3.1.1-os.html#_Toc398718028

3.1.2.4 Clean Session

"...If CleanSession is set to 0, the Server MUST resume communications with the Client based on state from the current Session (as identified by the Client identifier). If there is no Session associated with the Client identifier the Server MUST create a new Session. ..."

3.1.2.5 Wil Flag

"If the Will Flag is set to 1 this indicates that, if the Connect request is accepted, a Will Message MUST be stored on the Server and associated with the Network Connection. The Will Message MUST be published when the Network Connection is subsequently closed unless the Will Message has been deleted by the Server on receipt of a DISCONNECT Packet "

There are also a couple of extra properties that define more details related to the LastWill (3.1.2.6 Will QoS, 3.1.2.7 Will Retain, 3.1.3.2 Will Topic and 3.1.3.3 Will Message).

I am not sure whether they should all be configurable over the PubSub configuration - probably.

3.1.2.10 Keep Alive

"The Keep Alive is a time interval measured in seconds. Expressed as a 16-bit word, it is the maximum time interval that is permitted to elapse between the point at which the Client finishes transmitting one Control Packet and the point it starts sending the next. ..."

MQTT 5 redefines these a bit:

https://docs.oasis-open.org/mqtt/mqtt/v5.0/os/mqtt-v5.0-os.html#_Toc3901048

Clean Session is renamed to Clean Start (3.1.2.4)

And they have added 3.1.3.2 Will Properties, which can define more details related to the behavior of the Last Will functionality .

Also Will Message has been renamed to Will Payload (3.1.3.4)