Congrats on car
In UK, we don’t ordinarily use a bike hitch, more tow bar mounted, these are available for the Glc with hands free boot (electric tailgate) we have the option of flange or detachable,
I have the tow trust detachable, whilst bumper cuts are required, their allbut invisible from the rear, unless you know it’s there, electrics swing under the bumper when not used!
I have item fitted and full function, though I’m conscious of not triggering.
I either flip down my cycle carrier, open boot, then load bikes, or start engine, both avoid opening boot into cycle carrier,
Which oddly enough, I’ve never checked if it would collide
There’s also the option of roof bar mount, though, in my case it lasted a single journey....
I had the cycle carrier from previous car and expensively tried to use roof mounted system, too much hassle fitting and removing in comparison.