A HDRI should technically be 'neutral'.
This !
HDRi should look flat, almost "ugly", and if it's saved at higher exposure, with overbright highlights.
At which exposure is HDRi saved to .exr/.hdr doesn't matter (it's linear after all), there is benefit for both approaches: averaged and physical. The former will give you sort of auto-exposure look where you can directly use it for look-dev, for example in Marmoset or Unreal. The physical will have exposure where the light source will have the same intensity as in reality. Such calibration requires either lightmeter (or shooting grey ball and calibrating in 3D by eye). The lighting is the same, but the latter requires you to setup exposure in your DCC app and you can keep A-to-Z photographic approach because HDRi will match your physical camera setup.
Btw, my biggest petpevie is people who are arbitrarily white-balancing and color-correcting HDRi so they look nicer (profiling camera if you don't like manufacturer's white point and color matrix is ok though). This should be avoided (and I've seen the guy do it on his HDRiHaven blog where he desaturated yellow in one example,etc..) because this affects the light, all post-production should be done on resulting image.
