I am invested in Nikon, so will only say what I know about their brand. The Z (mirrorless) lens mount is larger than the F (dslr) mount, which Nikon has used forever, so you can't put an F mount lens directly on a Z body, but there is an adapter called the FTZ or F mount To Z mount adapter. While you can put any F mount lens on the FTZ adapter then on a Z body, only the newer F mount lenses will autofocus and adjust the f stop automatically, in other words, be fully functional. To the best of my knowledge, if an F mount lens is AF-S, it will be fully functional on a Z camera.
As far as quality goes, you will not loose any Image Quality using the FTZ adapter as there is no lens in the adapter, it just moves the F mount lens a little further away from the sensor to properly size the image for the sensor. However, Nikon's Z mount lenses are considered superior in IQ and you will want to move to Z glass eventually to get the most out of the Z body. As far as performance goes, slower AF-S F mount glass like the 200-500mm f/5.6 auto focuses around the same speed whether on a dslr or mirrorless body. Newer AF-S lenses take about 2x as long to go from minimum distance to infinity using the FTZ adapter on a Z body compared to the AF speed on a dslr.
Hope this helps.