Strix Z370 Gaming E + i7 8700 HIGH TEMPS on idle

Yeah if temps are boosting that quickly I'd lean back toward a bad cooler contact. HWINFo was only showing it up to 4.4-4.3ghz in your test and it's already 90C+. The test may not be stressing it enough to get your cores maxed. Regardless, 90C+ under stock settings below the max CPU turbo boost frequency indicates something is wrong. Voltages, or more specifically vcore, would have to be off by a decent margin to cause such behavior.

If it helps, I recently replaced a CPU cooler because it was creating the same problem. It would run a little high at idle and placing any stress on the CPU would immediately jack the temps up. In pretty much any stress test I'd hit thermal throttling damn near instantly. It was a cheap AIO I picked up at like 65% off at one point. I suspect the pump died in it. Replacing the cooler immediately solved the problem. It's not completely comparable to your situation but it illustrates what happens with a bad cooler or bad contact for it. Temps will skyrocket extremely quickly.

I'd revisit the cooler mount again. In some cases I've seen mention of the mounting mechanisms playing poorly with certain boards. In a way where everything appears seated properly but, for whatever reason, the cooler doesn't contact the chip correctly. You usually have to pair washers (of the non-conductive variety, ideally) with the mounting hardware to fix it. I'd think damn near every board would be built to play well with stock coolers but assumptions aren't safe.

I guess resetting bios is worth a try. The easiest way to do that would be to unplug the power cable from the wall or back of the PSU (flip off the PSU switch too if you want), connect/jump the two bios reset pins together for ~10 seconds and plug it in again. From your board manual it looks like the pins are right above your system panel header. I'd recommend using a screwdriver to bridge the two pins (no sense fumbling with one of those tiny jumpers.... not unless you enjoy scavenger hunts). Alternatively, if you're blessed with a bios reset button push/hold that for ~10s after unplugging the system (don't see one in the manual for your board).

The only other thing I can think of is the board is faulty. Software monitoring is nice but it's at best a ballpark. Furthermore, it's reliant on the applicable sensors. Those could be reading out incorrect values. It would conceivably be possible for your monitoring software to claim the board or chip is running at X voltage, or Y temperature but it's either doing something else or reporting it wrong. In other words, take the monitoring readouts with a grain of salt.

You said you were picking up a new cooler. If it is arriving within the return window for the board I'd install it and see if your problem fixes itself. If you're 100% certain your cooler is mounted correctly and/or the new cooler doesn't fix the problem I'd RMA the board, to be honest.