I think these things may be true in the original idea of the four jhanas.
As @jesophzizys points out, there is a problem with relating sanna to vitakka when the four jhanas are placed in the context of the eight or nine samadhis. Sanna can’t completely cease in the second jhana if it exists in the formless attainments after the fourth jhana. I had a problem in my own translations for a couple years: I was translating vitakka (from Chinese) as perception and also sanna as perception (following the convention among Pali translators). I thought about it and thought about it. Researched vitakka and vicara in Abhidharma texts. And so on. In the end, I changed my translation of sanna to “conception/concept.” I broadened its meaning to something that encompasses the cognitive “sense” better in English and left vitakka as perception.
I think the meaning of sanna was being stretched to something mystic or subtle by Buddhists. I mean, what is being described in these formless attainments? Infinite awareness? Infinite space? Nothingness? They sound like mystic experiences to me. But those experiences were then conceptualized as formless heavens the same way the jhanas were mapped onto the Brahma heavens. These two things, meditative experiences and the heavens, are intertwined in Buddhist thought. I think ancient Buddhists must have naturally assumed some heavenly place was being directly accessed in meditation, similar to the way Greeks thought Muses put ideas into their minds to explain the creative process. The four jhanas were the road to the Brahma Heaven because often visiting those places in meditation led to being reborn there.
But was that in early Buddhism? I don’t know. Maybe not. So, we have this problem of dealing with different (and ill-defined) historical strata in the Buddhist corpus that don’t always match up seamlessly. Translators end up agonizing over these issues because we naturally want to translate words uniformly and consistently for an audience in the here-and-now. But the texts themselves don’t always cooperate with us because they were written over the course of centuries. And a translator also wants to respect the original author (or, at least, I do). So, there’s compromises that have to happen. Translators are rarely “happy” with their work. If they are, I have to wonder what they are really doing.
The other problematic angle to me is in our English-speaking heads: We think it terms of five senses, not six. Which is why my analogy above uses a concrete an example of seeing an external event like an animal skittering by on a path. We have to stretch our way of thinking to consider cognitive processes as being sensory.