Note: I have retracted my proof from the Gemara in Sanhedrin 92a,b. I explain my newfound understanding in my comments to Deuteronomy's Answer.
First post here. I'll keep this as short as I can. I have Apeirophobia. Check it up (There's virtually no medical recorded information about this phobia historically, and its (granted, rare) occurrence among people like me, seems to be a completely modern phenomenon. In my opinion, it's less a "fear" than it is a truly warranted terrible "dread" of the existential possibility of eternity. There is much mention throughout the Torah and Rabbinic Literature about "Olam Va'ed" and "Netzach Netzachim" implying that the Afterlife or Days of Mashiach will last forever/never end. However, I know of two sources which seem to imply we will not exist a truly "never-ever-ending existence".
a) Adon Olam prayer: "V'achrei kichlos hakol, levado yimloch norah." - "And after the termination of everything, He (God) alone will rule awesomely." Edit: I simply don't see an interpretation of these words through the vague (and controversial?) Kabbalistic concept of a perfect world and God being one as fitting with the words. It clearly says, "after the finishing of everything" (contextually referring to the creation of any form). According to the kabbalistic interpretation nothing is finished, if anything it only reached the climax! Actually, as I write I am realizing that the word "Kichlos" might not necessarly refer to "termination" as I wrote above. Maybe it just means "completion"! Still, even so it would not work with the simple meaning of the verse since the word "Levado"-"Alone" isn't the point according to the Kabbalistic understanding. The point is "As one". Lastly, the words from the immediately preceding verse: "L'eis naaso becheftzo kol, azay melech shemo nikra." - "At a time when everything is done (obviously not in the termination sense) through his will, then 'King' his name we will call." those words seem to be referencing the climax of existence, the time when everything will be brought to its final purpose. There it seems more appropriate to apply the Kabbalistic interpretation.
b) One of the Ani Maamins: "Ani... Shehaborei yisborach shemo, hu rishon, vehu achron." - "I believe... That the creator blessed be his name, he is first, and he is last." This seems to imply that only God is actually eternal in its ultimate sense. (Interestingly, the Rambam doesn't mention the "last" aspect in his original formulation of the 13 principles. Edit: According to the simple understanding of this Ani Maamin, the "being the first" should perfectly contrast the "being the last". I think it's certain that the meaning of "first" is even pre- the Kabbalistic unified existence of God. And I suppose the average Kabbalist would agree to there having been such a time. In that case, it should be assumed that the "Last" means The same thing. This is also clear from another perspective. Just look at the declaration as a whole. It is quite clearly declaring the Existence of God, absent of ANY OTHER existence, both pre other beings and post other beings!
Also, though I can't point to anything off-hand, I believe that regardless of the subject of "eternity of the afterlife", there are numerous places in the Torah where it says "leolam va'ed" and according to the simple explanation it doesn't actually mean "true eternity".
Lastly, we know of the din "Moridin v'lo maalin" - "Being placed in hell and never lifted out of it, even after 12 months" which applies to heretics and certain other cases. Regardless of the basic argument from Apeirophobia, since God judges "midah k'neged midah" - measure for measure, wouldn't actual eternal/never-ever-ending hell be disproportionate to sin which is finite? Or maybe denying God/who is infinite, is considered an infinite sin? This thought can make me tremble to floor and go insane. I can't imagine anyone suffering for all eternity, even someone like Hi*ler yemach shemo. People don't get just how long eternity really is! It actually NEVER ends!
Please offer your insights.
Edit: I am now going to add some material of my own in regard to what Judaism says about this subject.
First there's Rebbe Nechman. One of Rebbe Nachman's most common themes is the concept of Lemailah MeHaZman. I am not sure exactly what he means by it, and there may even be slightly conflicting implications here and there, but an actual fundamentally different type of existence is definitely one simple way of understanding Rebbe Nachman's words. This view seems to be backed up by his brutal slamming of time in our world. He explains that the wiser one becomes the more they realize that time is inherently deficient.
Secondly, there's evidence (which I reinforce above) from Adon Olam and the Ani Maamin that there will be an end.
Third, I was very suprised to discover that there is actually only a handful of times (less than ten I believe) in the entire TaNaCH, that it's written "Leolam Va'ed"! I thought it was in the hundreds! I didn't have time to study them yet but half or so of them are in psalms, which to my poor knowledge MIGHT allow for excusing the words as "poetic depictions of all of time" (but not actual never-ending time).
Fourth, when it comes to all discussion of what will be in the end of days, the Rambam in, I believe to remember, his commentary on the Mishnayos, says that all opinions about how things will be in the "End of Days" are merely opinions. That is, he says that even the things that the Gemara says are not guaranteed!
Fifth, God's ultimate name YKVK, is the combination of his most distinguishing characteristic. Always was, is and always will be. This theme permeates through the entire Torah. I think that to say that us souls will live eternally, possibly takes away from the uniqueness of God in that respect.
That's enough for now, I may add more soon, but I think this is enough to indicate that it may not be so "clear" that eternity is a fact in Judaism.
Edit: Another proof is from the Gemarah in Chagigah 11b. It says 'One who thinks about what is above the world, what is below, what was before and what will be after, it's better that he never came to the world." This clearly seems to indicate an end.
You may ask what about the psukim which use the word "Netzach"? Well, what does Netzach mean exactly I ask back? Well, I tell you that what I do know is that the word is not intended to mean a literal eternity. I know this because many psukim use the word in context of complaining to God about "never-ending" suffering or lack of judgement! That can't be literal! Also, there's a pasuk comparing the eternity of the righteous to the stars. If eternity is literally "never-ending" then that's a really weak comparison. We know stars die. Even after they turn into a black hole they slowly evaporate. See link https://www.stsci.edu/~marel/black_holes/encyc_mod3_q10.html#:~:text=Since%20nothing%20can%20escape%20from,their%20energy%20to%20the%20Universe. and https://www.forbes.com/sites/startswithabang/2020/03/24/sorry-stephen-hawking-but-every-black-hole-is-still-growing-not-decaying/?sh=39113c8ad567
New Edit: It's worth noting that I just discovered that the Rambam himself in the Moreh 2:13 writes that time itself was created by God!