I found some terms like (non)ergative, inchoative, but neither quite fits the type of transitive verb that can do without an object, for example, "eat"
Have you eaten?
I ate an apple.
Is there a name for this type of verb?
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These can be called agentive ambitransitive verbs.
Transitivity is a hard concept to handle. Verbs like eat or drink seem like prototypic transitive verbs, but they occur in a lot of structures
And verbs like run or walk seem like prototypic intransitive verbs, but they can also occur in a lot of structures
And we can sense that there's an object implied with eating, though what that object is can't always be determined, because eat is a destructive verb, unlike (say) make. There's no clear noun phrase object with run, though the activity can be measured, and the measurement can feel like an object, though it isn't really a patient.
I would say that run is not usually transitive, except as a causative (run a business, run the donut machine), whereas eat has a direct object that can be referred to, like the agent in a passive. Eating is a human action, like running, but it requires props as well as a stage, and the props can be important, or they can be ignored.
I would also say, as I have said before, that transitivity is a property of clauses, not of verbs, though some verbs are almost always transitive, and others are almost always intransitive. But it isn't a natural classification for verbs -- the phenomenon is not binary and there are dimensions and degrees.