Hello V.,
For that, the short form (with [*]) should not be used, but rather the long forms with stereotype, as:
@startuml
state start <<start>>
start --> Active
note left of start : this is a short note on start
Active --> Inactive
note left of Active : this is a short\nnote
note right of Inactive
A note can also
be defined on
several lines
end note
state end <<end>>
Inactive --> end
note right of end
note on end
end note
@enduml

Enjoy,
Regards,
Th.