But what I wanted is to put "a name / heading" to the ideas these verbs refer to, i.e., what they express: the writer's feelings, state of mind (?), comment, denial, thoughts... But it is true that I can classify them the way you did, that is according to the types of clauses that follow them.
It is true, but you may be only making a list rather than creating any kind of meaningful classification. We can use the same headings for direct speech, and we can make nearly as many compartments as there are verbs, if we wish.
6. lack of continuity -- interrupted, interposed, interjected 7. expressed opinions -- thought, opined, reasoned, considered 8. solicited response
I'm sorry I mistook what you are questioning. All the verbs I showed belong to so called "verbs of saying". Reporting verbs are part of the "verbs of saying", which take a direct discourse and a that clause as its complement. I don't know what way "verbs of saying" are further categorized into groups. The verbs like "guess", "think", "believe", "suppose", "expect", "imagine",