Here is a personal experience.
I have a machine with an i7 6700. 16GB RAM.
I can run 8 Mirror Mode bots at 100% CPU and my cooling solution is good enough that im not thermal throttling on the CPU.
My ram is sitting at about 9GB Usage.
https://imgur.com/a/tVuAJKi - Proof of performance.
It should be noted that when the clients are loaded up and are idle (no script running at this point) CPU usage sit 55-60. Once all the clients are running bots, thats when it shoots to 100%. So as you start loading bots onto your new build, start with 10, check cpu usage. go to 15, check cpu usage, and incrementally go up from there based on CPU usage left.
The script you choose will dictate massively the CPU consumption. Where possible, disable Paint.
The real kicker here is that if you haven't purchased already. You should go with an AMD build, the more Cores/threads the better.
A high performing CPU with great clock speeds isn't what you need. Runescape can be run perfectly fine on a 1Ghz processor.
As you intend to run a game that only utilizes a single core. The higher core and thread count will benefit you greater than a faster CPU.
128GB RAM is certainly over kill
This is not to say that a High speed processor WON'T benefit you. Just that your money is better spent on a CPU that has a lower clock speed and a higher core/thread count.
Realistically. The best CPU to run a mass bot farm on would be an AMD thread ripper.
EDIT: I realized I never really answer your question.
Using my i7 which has 4 cores 8 threads that is able to run 8 as a baseline. It would be safe to assume that you will run at least 16. As others have mentioned. 20 seems in the realm of possibility. 40 however, seems unlikely. If it were stealth injection. for sure. Mirror Mode is a resource intensive beast. and again, The script your running will really determine what's possible.
I would like to stress that at this point if you planning on running a massive bot farm and have invested this money into a PC build, ensure that you have invested in a suitable cooling solution for your CPU.