I experienced some stuttering as well with my brand new build (5950x on Aorus Master x570s). It would manifest while gaming after several hours of up time, and go away after a restart, only to come back gradually and get more pronounced. It would also happen under Windows.
I did not get any thermal grease on the cpu pins, like you did, but I doubt this would matter if cleaned properly. You should be more careful when handling the CPU. Use some rubbing alcohol and tissue paper to remove it, and wait for the alcohol to evaporate before inserting the CPU. This works really well with thermal grease.
As for my stuttering issue. I thought at first my DDR3200 RAM kit was just too slow and something was not syncing. I bought DDR4000 RAM and the problem was still there, although it seemed less pronounced. I tried all kinds of CPU settings in UEFI in the process of troubleshooting this. Then randomly one morning my video card fans went full bore as I booted my computer, and the screen remained black. I reset the computer and it booted, but did the same thing as soon as windows loaded.
I ended up turning off the power, disconnecting the outside power cord and reseating the GPU. I remembered this had happened to me with this particular GPU in my previous computer, once in 5 years of use, and I attributed it to some random electrical issue.
My PC was working fine again, and, lo and behold, my stutter has been gone since.
I guess I'm sharing this to encourage you to explore beyond your CPU/RAM for possible causes of this. Your PCIe bus could be causing this, for example.
I still don't know if my issue was caused by this, because I didn't test to confirm. It could be coincidence. Another thing I did around the same time, which you might want to try, is to download the latest chipset drivers for your motherboard from AMD. You can check to see what version you motherboard vendor is providing you on its own site, and if the version is different on AMD's site, I recommend giving those a try.
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Ryzen 9 5950X - Scythe Fuma2 - Gigabyte Aorus X570s Master Rev1 - Gskill TridentZ Neo F4-4000C18-32GTZN