I am working on this as well. Funky here too, but I just had a breakthrough.
My process in version 3.8 is to diagnose where the issue is:
1. Export as KML (I have tried to set the CRS many different ways) MAKE SURE you have SAVE LAYER checked so that you get the layer exported in right beside the one you have exported from.
2. Turn visability on and off to see if the new, exported layer in QGIS is in the right place.
3. Mine often is not... even in QGIS! so...
4. Open Properties to see Information of the layer.
I started to realize that even though the CRS was the same, the Extents were reversed!
I am not sure why an export to KML would do this but to solve the issue, I started to set my CRS on export, as the more specific CRS. (In my case it is
Original Info from imported KML layer, which looks located correctly in QGIS:
CRS
EPSG:4326 - WGS 84 - Geographic
Extent
-82.5787124633789063,38.4103965759277344 : -82.5669479370117188,38.4228591918945313
Unit
degrees
Here is the exported using the CRS WGS 84:
CRS
EPSG:4326 - WGS 84 - Geographic
Extent
38.4103999976518011,-82.5787103514051068 : 38.4228528252385004,-82.5669500152173015
Unit
degrees
See the difference?
So, if I now export into KML and select CRS of WGS 84 [32617] (UTM Zone 17N), I get this again form the layer that was exported, BUT saved as a new layer in QGIS.
CRS
EPSG:4326 - WGS 84 - Geographic
Extent
-82.5787103514051068,38.4103999976518011 : -82.5669500152173015,38.4228528252385004
Unit
degrees
See! Extent shows exactly the opposite.
Like you, I am pretty new to this and learning everyday. I do not know what this means, what it is for, or even if it is a bug, but it is certainly not intuitive.