First of all, never farm with so such low resolution, that you cant see whats happening on the screen. Eventuelly you will get "bot checked" and if you cant see that, your accounts will be banned one by one, or worse. Personally i need a size around "1/4th of a 24inch monitor", per game, to sit relaxed back in my chair to clearly keep tabs on all my games. I can push it to 9 games per 24inch monitor, but it was really eyestraining, so i stopped. Even with 4 games per 24inch it feels like a "full time job", passing over from one game to another. Blizzard only give you around 10-12 mins to "respond", based on my personal experience.
So if you run 40 accounts: 12 min x 60 sec = 720 secs / 40 games = 18 secs per game.
So you will basically have very little breaks for your eyes. They will get sore. I hope you wear anti glare pc spesialized glasses. I cant imagine what it would be like to go from one small game to another on two HUGE "tvs".
Personally, lowest i want to play is at 1080p, 60 fps front, 20 fps back, with all on lowest possible and few addons, as you mentioned.
A 6 core (12 threads) cpu will be "good enough" for farming, per 10 games. 12 / 10 = 1,2 per game (the last 4 games will need to share 1 core/ 1 thread with other games).
So the amd 32 core has 64 threads. 64 / 40 = 1,6 per game. This should work ok. 8 of the accounts will have to share cores with other games. Ideal minimum would be 1 proper core per game atleast (and its 1 hyperthreaded partner) but the cpu has 32 cores, not 40. Do not expect stable and high fps while passing thru busy cities and such. Basically if its a busy time of the day/week, its most likely best to stay away. If you have to have a "heartstone" set at a city, place it on the other edge of the city somewhere, with low player activity.
Each game can use 2 gb RAM each at peak, so 40 x 2 = 80 gb RAM, so 128 gb RAM will be plenty enough.
All pretty good so far, but, and this is the problem,as i see it, the GPU:
At minimum, you want 0,5 gb vram per game.
If you get a amd radeon 7, which has 16 gb vram: 16 / 0,5 = 32 games.
If you get a 2080 ti, which has 11 gb vram: 11 / 0,5 = 22 games.
Cheapest and realistic solution (okey enough gameplay/fps for farm, run farm raids on your own and such):
Play up to a 20-24man: (approx 5000 dollars for parts except the case, win10 and peripherals).
And you can use the FTL playing method if you want. Get the 32 core /64 threads amd cpu, the radeon 7 16gb vram gpu, 64 gb RAM and a decent 1tb nvme ssd. 1000 watt or higher gold+ rated or higher powersupply. 3 x 12 fan AiO or similar.
Expensive solution for 40 for farming: (decent enough): (approx 6500-7000 dollars for parts except the case, win10 and peripherals).
32 core / 64 threads amd cpu, 128 gb RAM, the Nvidia Titan RTX gpu (24 gb vram / 0,5 = 48 games). 1200 watt or higher gold+ rated or higher powersupply. 3 x 12 fan AiO or similar.
Most expensive solution for 40, with "best" results: (ideal): /phu, this will probably cost a lot.
Wait and get the future 64 core / 128 threads amd cpu, 128 gb RAM, nvidia titan ceo edition 32gb vram gpu (or better). 1500 watt or higher gold+ rated or higher powersupply. 3 x 12 fan AiO or similar.
Do note that prices vary wildly, i just pulled these numbers of "pcpartpicker". In the country i live the amd cpu alone cost 2600 us dollars.
*i hope you are running fiber internet.
With your budget, you wont be able to get the 32gb gpu any time soon, and i guess you want to keep some of the budget for the monitors etc. So if i were you, i would choose the "expensive solution" i suggested above. *If you are in a hurry.
If you are not in a hurry, start creating the 40 accounts. Did you factor in the fact you need to buy 40 x bfa?, thats around 1400 dollars: and get them semi sorted on your current pc, macros, buy them better bags and move them to a location with a training dummy, etc. This way you are ahead a bit, when you later on plan to buy and use the upcoming 64 core cpu.
TL

R:
1.
yes you can play 40 games on 1 pc right now, it will be ok enough to "farm" with. Choose the "expensive solution for 40 for farming" solution above. Though i suspect you will go down to a 20-24 man, for the increased performance later on and get another similar pc, to play 20 + 20. For a 20-24man, this pc will be very nice.
2.
If you can wait, get the upcoming 64 core cpu from amd instead. More core/threads is king.
With this cpu you will be able to assign 2 proper cores and its 2 "hyperthreaded" part to the main game and some other + 1/"1" to each slave game = big yey.
More news if this 64 core comes out in november 2019, according to amd.
Edit:
yes, use your old pc as the "streaming pc".
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