What is the best CPU specs for running After Effects smoothly?

TL;DR:
you're not gonna get much better. If you can, switch to CS6 somehow.

adobe has made all previous versions inaccessible. Basically, they stole corporate secrets and what was supposed to be proprietary software sometime around the end of CS6 and the first year or two of CC. they got sued to hell and lost, and had to stop using the software, but put out an announcement saying they were passing all liability of corporate property theft to their users and that dolby or any other company could sue individual users for using basically any past version. They kept the ball rolling to force people to keep updating the software. This means, so long as new users have no access to previous software, and all current users update automatically, they don't have to worry about releasing bad versions because no one can know!

but I have both installed permanently.

without, then with multiprocessing in CS6 ---  8:43 and with multiprocessing 7:06

without, then with multi-frame-rendering in AE22 ---  8:43 and with multi-frame rendering 9:04

As you can see, the current version, after "a decade of optimizations" is between 0% faster, and 22% slower than versions released in 2012.
in more qualitative tests, 6k playback in CS6 was between 18fps and 11fps, while it was between 16fos and 9fps, and after 6 seconds, dropped to .6fps in CC22

as well, https://www.pugetsystems.com/solutions/video-editing-workstations/adobe-after-effects/hardware-recommendations/ here's an advanced breakdown on how to build one. (hint, the optimal computer for AE stopped existing in 2008.)

"After Effects used to make great use of high core count systems (including dual Xeon) but starting with AE CC 2015 most tasks no longer benefit from having a high number of CPU cores. This is largely due to the fact that Adobe removed the “render multiple frames simultaneously” feature"

-hits the nail on the head. even the latest multi-frame rendering is just a hack that copies the process to every core, and is less efficient than whatever they were doing in 2015. and don't kid yourself- only a handful of effects use GPU at all. most aren't even 16 bit color compatible. jump ship if you can.

so get CS6, you'll only be a little disappointed. You can't get keys very easily, but I hear if you're willing to sail the high seas, you can find treasure for free.

None of this means anything if you don't provide the actual specs of the machine, details about your render settings, contents of the composition/ project, settings for caches, multiframe rendering and so on. That said, no, there isn't a mythical super PC out there that will make everything in AE go realtime/ smooth. It's just not how the program works.

Mylenium