Is samsara without end?

The answer

"Anamataggo" word is in S.N. Nidanavagga = cause = paṭiccasamuppāda = cycle loop of causes and effects.

You must recite and memorize it's pāli, before you ask something about pāli. The answer already appear in sutta sequence, but you overlook it because you never recite and memorize it's original pāli.

The analysis of anamatagga word

Why the translators try to translate like that?

Because of pāli context of this sutta forcing them to do like that.

Pāli's sutta:

"Anamataggoyaṃ, bhikkhave, saṃsāro. Pubbā koṭi na paññāyati avijjānīvaraṇānaṃ sattānaṃ taṇhāsaṃyojanānaṃ sandhāvataṃ saṃsarataṃ."

The translators must describe "Anamataggo" like:

"Anamataggoyaṃ bhikkhave, saṃsāro == Pubbā koṭi na paññāyati avijjānīvaraṇānaṃ sattānaṃ taṇhāsaṃyojanānaṃ sandhāvataṃ saṃsarataṃ."

So, in commentary:

anamataggasaṃyuttassa paṭhame anamataggoti anu amataggo, vassasataṃ vassasahassaṃ ñāṇena anugantvāpi amataggo aviditaggo, nāssa sakkā ito vā etto vā aggaṃ jānituṃ, aparicchinnapubbāparakoṭikoti atthoฯ saṃsāroti khandhādīnaṃ avicchinnappavattā paṭipāṭiฯ pubbā koṭi na paññāyatīti purimamariyādā na dissatiฯ yadaggena cassa purimā koṭi na paññāyati, pacchimāpi tadaggeneva na paññāyati, vemajjheyeva pana sattā saṃsarantiฯ

However, some pāli students maybe over worry about "how to make 'anamatagga' by kaccāyanasutta (ancient pāli grammar cannon)", then they will be stuck their thinking with anamatagga's ingredients. This is just the first rule of vicayahāra in netti-pakaraṇa cannon, pada-vicaya. But commentary can going on by next rule of vicayahāra in netti-pakaraṇa cannon, pubbāpara-vicaya, then use "54, 60 jinavacanayuttaṃ hi" and "404, 370. tesu vuddhilopāgamavikāraviparītādesā ca" of kaccayanasutta to translate 'anamatagga'.

So, if you recited and memorized pāli, first, you will know this process and leave out of being stuck in pāli's ingredient.

A sutta like this ("the skeletons of a single person, running on and wandering in samsara for an aeon, would make a heap of bones, a quantity of bones as large as this Mount Vepulla") or this ("would that blind sea-turtle, coming to the surface once every one hundred years, stick his neck into the yoke with a single hole") implies that it may be (or may have been) a very long time indeed.

It's not clear whether that long time is past, future, or present.

IMO the implication is that it has been a very long time in the past, and that unless you start the follow the Buddha's way (for liberation) it will continue indefinitely (until you do).

The question of whether it's literally endless may be another of the unanswered questions ("Is the cosmos eternal?").

Well, from Mahayana perspective it's both. Samsara is endless, just like Dukkha is an invariant principle of sentient existence. Accepting Dukkha (here, inherent unreliability) of phenomena makes it Tathata, suchness. Accepting Samsara makes it Nirvana. Does not mean Samsara has ended or Dukkha ended - not at all. We just make an end to it (nirodha, 3rd N.T.). Endlessness of Samsara is one thing you can truly rely on, which makes it unconditional Nirvana.

Now, if I forget all that and just reason from the original sources, here is what I get:

Looking at your PTS dictionary quote, they are talking about Anamatagga (without beginning / without end) being an epithet of Samsara. When I search Sutta Central for "anamatagga" I find for example this verse from Therigatha:

"...Long are the foolish in Samsara,
again and again cry
without beginning, without end, over the father's death,
the slaughter of the brother and the murder of the self.

Oh tears, breast milk and blood:
without beginning, without end you run in Samsara!
Remember the wanderings of the creatures
and the way the bones pile up!

Remember the four oceans,
filled with tears, mother's milk and blood!
Remember in one epoch
bones heap up like mount Vepulla!

Without beginning, without end have you flowed (lit. samsara’ed),
endless like the seeds of jujube fruit. ..."

This, combined with the literal meaning of the word "samsara" - "running by itself", "drifting" can point us in the right direction. Samsara is endless unless we put an end to it (nirodha). And how do we put an end to it? By applying the principle of this/that-conditionality and undoing the 2nd noble truth, i.e. by accepting what is and arriving at tathata. Now technically, what we accept is not really Samsara as it is, that would be surrendering. Instead, we learn to see Shunyata and that's what we accept, Samsara-as-Shunyata. Does not mean that Samsara has gone anywhere though, it is still endless as it always were. In fact, if we want to help other sentiment beings, we have to deal with Samsara every day.