It is far more than just slightly tilted unfortunately. Yes, it’s in the EBT, but my personal impression is that the Buddha had little business discussing the teachings of other people. At several places (maybe not all) when other teachings or Niganthas are mentioned it is relatively simple to show that these were later additions.
Because of the almost monopoly status of the EBT on meditation it may even seem to the casual reader that the Buddha invented meditation altogether! This is most probably not true: the EBT admit Gotama’s two teachers with high ‘arupas’ and at one point Nataputta rejects the idea of a second jhana - implying that he knew of the first.
Both terms, samadhi and jhana, are probably of later / samana origins: samadhi starts appearing in late Grhya- and Dharmasutras and later in the Sanskrit Epics. An exception is dhyana (Skt. for jhana) in Chandogya-Upanisad 7.6, 7.7 & 7.26 (a later part of the Upanisad) - I think correctly translated as ‘deep reflection’ by Olivelle in this context.
So the terms are probably of sramanic origins and it’s futile to look for them in older literature. An exception is the Atharvaveda with all its difficult transmission where ‘dhyana’ is mentioned in AV 2.34.3, AV 18.2.47, AV 20.88.1. It seems in meaning somewhere between ‘deep reflection’ and ‘meditative contemplation’.
But this was not your question. The terms might appear, but without reference to a technique. My impression from the ancient brahmin texts is that there were two sources that can be perceived as ‘meditation’: a. the equivalent of ‘right view’ and reflection upon it and b. austere practices aiming at a trance-like stillness of mind.
Regarding a. you can find very often in the early Upanisads first an esoteric revelation and then the formula ‘who knows this…’, and then something like ‘attains immortality’ or so. We must assume that this involved a deep reflection by the students, the effects of which we can easily imagine as similar to a first jhana - repeating, immersing, delighting in the words, becoming one with them, etc.
The trance-like meditation of b. belongs to the category of ‘tapas’ practice, a set of ascetic, often physically demanding practices in which - we again must assume - ecstatic or trance-like states were achieved. The quality of tapas is fiery and has tremendous determination as its root. Through dedication and pain purification is achieved. This is known from the times of the Brahamanas on (much earlier than Buddhism) and the Atharvaveda.
Often before the main rituals people had to ritually purify themselves through preliminary rituals and tapas-practice. It is said that under the right circumstances tapas draws closer the presence of the gods. Again we can imagine that this was accompanied by extraordinary feelings or visions.
Sacred fasting was a tapas practice, but also standing motionless, lying on the ground in the sun without moving etc., i.e. exertion and endurance. It is not clear unfortunately what happened mentally, but we can assume that like the body also the mind was stilled. If you stand on one spot motionless for hours you have to somehow deal with pain, either trance or meditation. But surely you develop a certain understanding and skill with the mind - be it ultimately fruitful or not.
It’s also easy to draw a line from the brahmanic tapas practice to the Jain practices of pain endurance, being motionless and avoiding any karma. A basic idea is through these practices to overcome the human condition rather than to realize its potential. With this in mind it is not very surprising that austerities were the initial practice of Gotama (although I would not take the suttas literally on this).
I didn’t include many references here but the above is not really controversial. A good overview can be found in Kaelber (1989): Tapta Marga - Asceticism and Initiation in Vedic India.
Regarding the Jain texts it’s really unfortunate that there is not nearly as much and good recent research as with EBT studies. Many of the scholarly assumptions are over 100 years old and I wouldn’t rely much on it. My personal impression of the literature (Oldenberg’s translations are available) is that they are partly indeed old and don’t show obvious meddling as with the EBT. As with many EBT suttas that I hold as very old also many Jain sutras are not technical but inspirational.