I don't know why you bring up unstable. RAM is not unstable, the problem is RAM is sold in kits, or packs of sticks that work together. Mixing kits is using incompatible RAM and as a result, the sytem may be unstable or ever refuse to boot.
But you have to deliberately do something you're not supposed to do (mix RAM kits) for this to happen.
If you remove a cooler from a CPU, it will also be unstable but only because you did something you're not supposed to do.
To your question, DDR5 or DDR4 or DDR3 are all sold in kits. Usually 2 sticks to a kit but sometimes 4. 2sticks run faster than 4 but not more stable. They are all stable. The only exception is mixing sticks from different kits. That may even work but it's not something that should be done.
The reason DDR4 is prefered for your case is because you want 128Gb. There aren't that many DDR5 4x48Gb or 4x32Gb kits, and the ones out there cost a ton of money. DDR4 kits are cheaper and more numerous.
DDR5 is a little bit faster but a) a lot more expensive, and b) not so much faster when shopping 128Gb kits.
I really appreciate the lively discussion here. Right now, I'm planning to get this 128GB set:
https://pcpartpicker.com/product/HK...-gb-ddr5-5600-cl40-memory-cmk128gx5m4b5600c40
What motherboard are you planning to use this kit in? If it's not compatible with your motherboard, you'll have to send it back.
Also, there's a reason that kit costs around $450 and other kits are nearer to $700-1000. It's not because it's better.
Take my advice, and buy a 2x64Gb kit of DDR4 or DDR5 RAM, preferably DDR4. Use a DDR4 z690/z790 motherboard that lists your chosen 2x64Gb kit on it's QVL. If the motherboard manufacturer doesn't list it on the QVL, then check with the memory vendor. If it's not listed, don't buy it because it may be incompatible.
If you buy it anyway, it's a complete shot in the dark.