As discussed in the linked post, the issue here is not that instability in higher order pseudoknots is unrecognized, but that the requirement is just that any pseudoknot is present (regardless of target structure) - if you have one stable first-order pseudoknot and one instable first-order pseudoknot, that constraint would still pass.
I believe the desired behavior here would be a mechanism to indicate whether the natural mode does not match the target mode, even if it is not “required”. Happy to discuss further if you feel this is insufficient for your use case!