The camera doesn't work on the current XPS13 if you upgrade to a 6.X kernel (which, to be fair, means moving outside of Dell's packaging.) Technically this is Intel's fault, as they haven't released firmware for it yet. Still, hopefully the Dell team avoid similar issues in future configs by ensuring better driver support. It's a nice laptop otherwise.
My cam doesn't work on my 5 year old Inspiron either. It's one of the reasons I'm not buying the Inspiron 16 plus in this moment.
I've owned several Inspirons and have no issues but then I use Arch (actually). Have a look into what kernels are on offer and consider a different one. However you may have another issue because I seem to recall that cams are now all basically standards based.
Try grabbing a couple of live "CDs" of other distros and boot them. See if your camera works. Try something like OpenSuSE "tumbleweed".