I am a retired software engineer who has worked in the field for nearly 30 years and I can make some pretty good educated guesses as to what Apple is saying.
Let's tackle the main reason I think Stage Manager is limited to M1's. What many people here say is correct in that the amount of real physical RAM and flash speed make a difference in terms of performance, but something just about no one has mentioned is that the A-series do not appear to have the controllers to handle virtual memory, an absolute requirement for Stage Manager to even begin to function. I'm sure most of you have watched a ton of YouTube videos where people have examined how Apple builds their SoC's. They put in exactly what is needed for their long term plans, no more and no less. They customize their SoC's according to their target plans, such as putting Thunderbolt controllers or ProRes encoders directly into the silicon to boost performance, or even interface transistors to help tie two or more chips together into a single SoC like the M1 Ultra. These are not general purpose processors.
Virtual memory is no different. Requisite controllers are needed to efficiently handle the tremendous amounts of RAM contents that must be moved to and from a swap file. You'll notice that there is no shipping OS that runs on an A-series SoC that supports virtual memory. So why does anyone think the capability is present in the A-series chips? Apple builds into their SoC's only what is required. Anything else is an unnecessary risk since space on a silicon wafer is extremely valuable. The bigger the die, the fewer the chips and the higher the chance of low yields. This is why the A15 chip is left out even though the cores are newer than those of the A14, from which the M1 is based.
It has nothing to do with the performance of its CPU or GPU cores, but has to do with its memory and storage controllers. If they aren't built to handle virtual memory's demands, you're going to have very poor performance without the hardware support. You can simulate all of it in software, but it's not going to have acceptable performance. As an example, hardware ProRes encoder/decoders are orders of magnitude faster than software ones, which the M1 had to rely on, but the M1 Pro/Max/Ultra and M2 benefit significantly from the hardware encoders/decoders built into them. The M-series chips have the required controllers while the A-series chips do not since the M-series chips were built to run a desktop OS where virtual memory is second nature. It was never a requirement for A-series chips to do the same.
Now there are those who bring up the A12Z in the developer's toolkit that managed to run macOS. However, the dev kit was not a shipping system. It had a processor that was the latest capable of running the same instruction set as the future M1 would. The A12Z was Apple's only choice at the time. But how did it run macOS? It didn't without the help of supporting chips. Like an Intel or AMD system, the A12Z wasn't the only chip on the motherboard.
Windows PC's have a zillion support chips to handle things that the CPU/GPU can't. This is why every new release of an Intel/AMD CPU is accompanied by a new chipset. Some may be familiar with the terms, Northbridge and Southbridge. Those are chips that handle I/O for the system because PC's are rather distributed and not concentrated into an SoC. So was the A12Z Mac mini dev kit. It wasn't a shipping system, so Apple engineers cobbled together parts to handle things the A12Z could not handle on its own.
Among that was optimized memory controllers to handle virtual memory. So just because a kluged machine that eventually ended up in the trash bin could run macOS doesn't mean A12X/Z iPads could as well. Those iPads weren't equipped with the support chips the dev kit had and therefore cannot run virtual memory. No virtual memory, no Stage Manager. And as some have said, the dev kit had plenty of real RAM, too. Even if someone were to hack the system to "enable" Stage Manager on A-series iPads, the result would probably be an instant crash or severe out of memory errors. The A-series simply do not have the necessary hardware.
Stick an Intel CPU into a system without its chipset and you get a non-functioning system. The same applies to the A12Z. No support chips, no Stage Manager. No single chip works alone, not even an SoC.
We all guessed last year that Apple stuck the M1 into the iPad Pro because they didn't want to bother making an A14X. I guess we were all wrong. Apple apparently had a roadmap and made sure the 2021 iPad Pros had the required hardware to run desktop-class OS features. Apple doesn't do anything without planning years in advance. One thing it guarantees is that future iPad Pros and Airs will continue to have M-series SoC's. It'll be interesting to see what future features Apple has in store for M-series iPads.
I am extrapolating what Apple's press release said based on a lot of years of experience and having watched the evolution of hardware systems from cheese wedge (early designs are done on a board that looks like a giant cheese wedge) to completed systems. I could potentially be wrong since I have no inside information. The strongest evidence is the lack of virtual memory on any A-series OS which points to a lack of any hardware support, especially with the omission of the A15. Feel free to disagree, but this explanation seems to fit what we know. If you do disagree, tell me why. Please no, "it's because I feel they're lying" arguments. That's just a waste of time.