Currently it is not possible to define formally in a state machine diagram that a behavior linked to a transition/state triggers a message to be sent through a port.
I think that being able to formally describe this would in fact make this kind of diagrams very valuable for compositional verification of state machine diagrams. See "Towards the Compositional Verification of Real-Time UML Designs" by Holger Giese et al. for reference

This issue is not entirely clear, but it would seem that the desired capability is available by using an InvocationAction
with onPort, as now described more fully in the UML 2.5 beta specification in Subclause 16.3.3, under “Invocation
Actions and Ports”.
Disposition: Closed - No Change

There isn't a constraint that prevents multiple associations from being specified between the same Actor and Use Case. Multiplicity is handled already by the multiplicity at the association's ends, so having two or more different associations seems to be redundant.