As you use the predefined parameters option which only creates StringParameterValues.
This is due to the fact that it does not know any thing related to the triggered jobs, so does not match parameter types at all.
Note that downstream job should not have an issue as the boolean parameter is exposed as an Env variable as KEY=true/false.
The display of the Parameter in the triggered job is done via the parameter type passed to it not from what is configured from the job.
The only solution to this would be to implement a Boolean Parameter for the parameterized trigger plugin that passes boolean parameters.