Is the word "samsara" composed of simpler concepts etymologically or otherwise?

In lord Buddha's words "පුබ්බා කෝටි න පඤ්ඤායති"[Pubba Koti napangnayathi]. It means "I cannot find the beginning of the "Samsara". Lord Buddha Looked backward millions trillions of years but could not be able to find the beginning of the life. It is like a circle. In a circle we cannot find the beginning as well ending. But Lord Buddha taught us how to come out of the circle. That is attain Nibbana. To have better understanding you need to read and learn about Dependant Origination["Patichchasamuthpada"].

Read this article to find what happened to the person who traveled to find the end of this Universe:

1. Rohithassa Sutta
2. Loka Sutta

It is with ignorance (Avijja) as condition that formations (Sankara) come to be

This is the Wheel of Dependent Origination: . “1. Ignorance - avijjā Ignorance of the Four Noble Truths in particular. That is to say, not seeing the realities of suffering and its origin.

2. Volitional Formations - saṅkhārā Acts of the will in body, speech or mind. The making of karma.

3. Consciousness - viññāṇa Knowing the sensory objects through the six types of consciousness, i.e. vision, hearing, smell, taste, touch and thought.

4. Body-Mind - nāmarūpa The physical body and the three mental aggregates excluding consciousness, i.e. mental formations, perception and feeling. These together are sometimes called the mental body.

5. Sixfold Base- saḷāyatana The psycho-physical bases of the six senses. The sense organs and their associated mental factors.

6 .Contact - phassa Sensory impingement. The coming together of three factors; the physical organ, its object and consciousness. Example - visual contact is the coming together of light waves and the sensitive cells of the retina together with conscious awareness.

7. Feeling - vedanā Pleasant, unpleasant or neutral emotional reaction to sense contact.

8. Craving - taṇhā Craving for sense pleasures, craving for existence, craving for nonexistence. NB the link between feeling and craving is the key point where the cycle can be broken and liberation can occur.

9. Clinging - upādāna The intensification of craving to the level of obsession. Defilement is very difficult to deal with if it has been allowed to develop to this stage. Four kinds of clinging are listed; clinging to sense pleasure, to views, to rites and rituals and to the doctrine of a self.

10. Becoming - bhava Coming into existence or being. There are three levels of being; sensual, fine-material and immaterial. These correspond to sensory, jhanic and formless jhanic consciousness. Also to existence in the various realms. Sensual being includes the lower realms, human and sensual heavens. Fine-material includes the brahma realms and immaterial the realm of formless deities. NB nibbana is outside all of these realms and is not a type of becoming at all.

11. Birth – jati The emergence into one or another order of beings.

12. Old Age (jara) and Death (maraṇa) and also sorrow and lamentation, pain grief and depair; that is how there is an origin to this whole aggregate mass of suffering. This is called the Noble truth of Suffering. The inevitable result of being born.

For further learning listen to this videos:

1. Dependant Origination
2. Dependant Origination

Samsara is like this and lord buddha told us "I cannot see the beginning of the samsara of the creatures" Like in this picture we are traveling according to our Karmic results in other words the causes and the effects.

Until we understand the Ultimate realities and drive this journey to attain Nibbana. Hope this article may helpful for you to find the answer of your question.

May triple Gem Bless You!!!

Etymology

Questions on this site tend to be more about doctrine and practice and less about language. I don't know etymology beyond what you can read in a dictionary. Also I assumed the word pre-dated Buddhism, but Wikipedia says maybe not:

Some scholars state that the Samsara doctrine may have originated from the Sramana traditions and was then adopted by the Brahmanical traditions (Hinduism). The evidence for who influenced whom in the ancient times, is slim and speculative, and the odds are the historic development of the Samsara theories likely happened in parallel with mutual influences.

Meaning

I wonder if an equivalent modern metaphor might be "hedonic treadmill" i.e. chasing after pleasures.

I think of Samsara as depicted in the Wheel of Life and driven by the Three Poisons.

Buddhist text -- what text is it and/or what do they generally say?

In brief I think I've read them say that there's a lot of it (of samasara), and that it's not entirely happy or keeps being sad (because of loss).

This page on Access to Insight includes three sutta references.

There are other references to Pali texts -- suttas but also other texts like the Visuddhimagga and the Dhammapada -- in the definition here. Those references aren't hyperlinked, and they're in a slightly non-standard format or numbering (or by "non-standard" I mean, "there's more than one standard"), which I find makes lookup a bit tedious -- but I think that the first reference for example i.e. DN.i.54 corresponds to DN 2, where (as it happens) it's quoting a non-Buddhist explaining his (non-Buddhist) views:

Pleasure and pain are allotted. Transmigration lasts only for a limited period, so there’s no increase or decrease, no getting better or worse.

The next is DN.ii.206 which is DN 18 and so on.

This topic might help if you want to follow cross-reference like that: Tripitaka Section Numbering

Saṃsāra, Anamatagga, "whose beginning and end are alike unthinkable"

Saŋsarati (Sangsarati): to move about continuously, to come again and again. to go through one life after the other, to transmigrate

Saŋsāra: 1. transmigration, lit. faring 2. to go through one life after the other, to transmigrate.

Saŋ ~ bond, put together, sāra ~ going, moving, following, fluid, flow, reed, an arrow.

usually used with Vattha, Samsara Vattha: Circle of ... endless seeking, asking on.

"Saṁsāra literally means “wandering-on.” Many people think of it as the Buddhist name for the place where we currently live—the place we leave when we go to nibbāna. But in the early Buddhist texts, it’s the answer, not to the question , “Where are we?” but to the question, “What are we doing?” Instead of a place, it’s a process: the tendency to keep creating worlds and then moving into them. As one world falls apart, you create another one and go there. At the same time, you bump into other people who are creating their own worlds, too." ~ Thanissaro Bhikkhu "Saṁsāra" https://www.dhammatalks.org/books/KarmaOfQuestions/Section0008.html