(1) It is
strongly recommended to update BIOS to the latest version, which is F5:
https://www.gigabyte.com/Motherboard/Z790-GAMING-PLUS-AX-rev-10/support#dl - This includes the very critical Microcode Update 0x12 for mitigating CPU degradation due to excessively high Core voltage. This is a well known problem.
(2) It is also recommended that you replace the ILM (Independent Loading Mechanism) with a "Contact Frame" which solves the problem of IHS (Integrated Heat Spreader) warping, and is also a well known problem. -
https://www.tomshardware.com/reviews/thermalright-lga1700-bcf-contact-frame - This can improve Core temperatures by as much as 10°C for about $8.
https://www.amazon.com/Thermalright...Full-Fitting-Installation/dp/B0BQF13FK1?gQT=2
(3) As has been pointed out, a low-end 4 Pipe Thermalright Assassin Spirit is
woefully inadequate for a high-end 14700K. Here's an excellent 7 Pipe Dual Tower air cooler for about $38:
Thermalright Phantom-Spirit 120 - A 280mm / 360mm AIO is preferred to tame the power hungry 14700K. The Lian Li 240mm AIO performs on par with many 280mm / 360mm AIOs:
https://www.tomshardware.com/reviews/lian-li-galahad-ii-trinity-performance-240-aio-review
(4) Changing thermal paste to high-end won't affect Core temperatures by more than a few degrees at best, and will not solve this problem, so the MX4 you're using is fine. But as has been also mentioned, set the Power Limits to 253 Watts, as per Intel's recommendations.
(5) "Idle" is defined as 1% CPU Utilization as shown in Task Manager. 5% is not idle. Unnecessary Startups, Background Processes and Services can be disabled in Task Manager to reduce CPU Utilization at Idle to 1%, and thus Core temperatures at Idle.
(6) Ambient (room) temperature directly affects Core temperatures. The International Standard for "normal" room temperature is 22°C or 72°F. Although it's summer in the Northern Hemisphere, if your A/C is set to 79°F, that's 26°C. If you're running your rig without A/C, then your ambient room temperature, and thus Core temperatures are determined by mother nature.
(
Q)
What is your ambient temperature?
(7)
"Choices on case were, unfortunately VERY limited since not including ANY hard drive or DVD/BluRay drive bays seems to be the (frankly disturbing) trend". I completely agree with you. Some users still prefer the convenience of an internal optical drive, which is fine. However, the Versa H21 is very restricted and limited in terms of airflow. The Cougar MX330G ($59.99)
https://www.amazon.com/Cougar-MX330-G-MX330-Tempered-Window/dp/B079X2P3TR has a 5.25" Optical Drive Bay, an open internal design for excellent airflow, and can accommodate a 240mm AIO. We chose the Cougar MX330G for my wife's rig, as she uses her Optical Drive occasionally. The cooling in this case is excellent.
At the very least, we recommend that you flash the BIOS to F5, check that Power Limits are set to no more than 253 Watts, install an $8 Contact Frame, and install a $38 Dual Tower air cooler, for a total of about $46. An optional but serious improvement would be moving to the $60 Cougar MX330G Mid-Tower case.
CT 