Notice the directed (paṇidhāya) samadhi , and undirected (ap-paṇidhāya) samadhi are referring to role of V&V in first jhana, and it’s dropping out in second jhana.
So the Buddha already has many terms and ways to express “placing the mind & keeping it connected”.
There’s also “manasi karoti” (paying attention), used frequently in the context of samadhi bhavana. For example, to develop perception of light for knowledge and vision, one pays attention to the sañña (perception) of light, whether by day or night.
There’s also "cetaso abhiniropanā " , directing of mind, used as one of the definitions for sankappa in MN 117.
In Bhante Sujato’s blog post explaining his view on V&V (vitakka & vicara), he makes it seem like the Buddha just didn’t have any other suitable words to express “placing the mind & keeping it connected”, so he had to sacrifice V&V and give it a totally different meaning than is used everywhere else in the suttas. Why would the Buddha do that and create so much confusion? And if he’s going to give V&V a new meaning in first jhana, almost opposite to it’s original meaning (see next paragraph), shouldn’t he explain the new meaning somewhere in the suttas? Ven. Buddhaghosa doesn’t show up for another 1000 years, and Bhante Sujato isn’t born for at least another 2500 years from when the pali suttas were composed. They’re not walking through the door to explain to the puzzled pali listener what that “placing the mind and keeping it connected” means. So where in the suttas is it explained?
The “cara” in vicara, the basic meaning of carati is roaming about, walking, exploring, wandering around, traveling. Cankamena is walking meditation. Vicara is the mental equivalent of that, exploring a topic selected by vitakka (directed thought). But in VRJ (vism. redefined jhana) and B. Sujato’s V&V translation, vicara takes on the opposite meaning! Instead of exploring and evaluating, it’s sticking like glue trying to not move and become completely still!
So why would the Buddha give vicara the opposite meaning in first jhana, and then not even bother to explain that the change happened (remember, the pali listener hears V&V, the same V&V he hears everywhere else, not the retranslated version), and nowhere in the suttas that actually explains the redefined meaning in detail.
Of all the many reasons the VRJ definition of V&V is wrong, this is probably the first, and most fundamental reason, why that is completely unsupportable. That Vism. insists on this, is understandable, since they’re trying to reinterpret the EBT to claim compatibility (non contradiction) with their idea of momentariness. But why B. Sujato, who champions principle of least meaning and ockhams razor as his guiding principle in translation? It baffles the mind.