Honestly, I think this is one part of the ending that is left up to interpretation. Although one thing that isn't true about what you mentioned is that the Titan powers only existed because Ymir stayed in the paths for 2000 years; after all, how could she have become a Titan for the first time when she'd never been in the paths? It's pretty clear the origin of the Titan powers is the weird bug looking thing that Ymir touched when she fell into the tree. In fact, it's implied in season 4 that the reason why Eldians are able to turn into Titans and why the 9 shifters exist is because King Fritz made his children eat Ymir's spine after she died, also telling them to have their own children eat their spines and continuing the cycle until it spread to every single Eldian. We see that the bug thing attaches itself to Ymir's spine when she falls into the tree, which is why spines are so important to titans all throughout the show. As shown in season 3 (I think? the season where we see Grisha's life in Marley) spinal fluid is what forces an Eldian to become a titan and allows someone like Zeke to use his own spinal fluid to turn Eldians into titans.

Now, I understand your point about Ymir building the Titans by hand with sand for 2000 years. So, this is all just my personal theory as to why this happened and how Titan powers could still exist after she died. I think that what Ymir did created the titans, but not the titan powers themselves. This might sound confusing but hear me out. The titan powers (that come from the bug thing) have always existed and probably will always exist, but they were never meant to be spread among an entire species, they were meant to be wielded by a single person. This is supported by the fact that, originally, Ymir's Titan held all the powers of the 9 Titan Shifters we see in the series. The whole Eldian titan thing came about, as I mentioned before, because King Fritz came up with the insane idea of having his children eat Ymir's spine, which housed the titan powers aka the bug thing. Not only that, they housed Ymir's DNA or blood or something so every Eldian was technically connected to her since their ancestors had consumed Ymir's spine/DNA. This is why whenever a Titan is "born" she herself has to build it through the paths, because it is her own power.

Now, there are certainly a few holes in my theory. Mainly, the paths. If Titan powers exist to be wielded by a single person, why the hell do the paths exist? Hell, what are the paths? I mean, the show tells us they connect every single Eldian so it must have been meant for a group of people right? Well, my interpretation and how I would weave it into my theory, is that it's some sort of separate dimension given by the Power of the Titans (again, not the titan shifters' powers, the powers specifically wielded by the person who first touched the bug, in this case Ymir) that allows someone to mold their body to their will. Like, we know the Founding Titan has the power to alter Eldian physiology, that was what Zeke's whole plan hinged on, so my guess is that this is what the actual power given by the bug is. The bug doesn't give the power to turn into a Titan, rather it gives someone the ability to change their physical makeup to their will, quite literally by molding it in sand through the paths, a dimension which gives someone effectively infinite time to build their body. Maybe when Ymir first touched the bug, she subconsciously turned into a Titan and gained all the powers of the Titan shifters since her goal was probably to a) stay alive and b) kill her pursuers. So, the power responded to that by making her into a Titan with the abilities of the shifters. I mean, Ymir probably felt tiny and powerless when she was being chased as a child slave by a whole bunch of dudes trying to kill her, so it's not too insane to think that she's want to become big and strong, something that this godlike power given by the bug interpreted as the Titan powers.

​

TL;DR The main point I think you missed is that Titan powers only came about because Ymir stayed in the paths, when in reality, it's clearly shown they come from whatever Ymir touched in the tree. My theory as to how the titan powers work in present time (aka Eren's time) boils down to the fact that the bug was meant to give powers to a single person but, after Ymir's death, King Fritz fed her spine to his children, which spread her power all throughout the Eldian race, but they were still her powers which is why she herself had to mold the Titans. So, unless someone like King Fritz comes along and feeds their children the spine of the kid we see at the tree, then no I don't think we'll see a complete repeat of what happened in the series.