I got the same thing on my custom-made PC with an NVIDIA RTX3060 card. We’re not alone: Trouble with 20250511 installer? - Bazzite. I had downloaded the Bazzite 42 Nvidia Open ISO, and was stuck on the white/gray screen.
I found that the Bazzite site also offers a BitTorrent link, and that it had not been updated to Bazzite 42 yet: it was the 41 version. I got that version by BitTorrent and the installation worked. I just wanted to try out Bazzite though, I knew I wanted Aurora because I had installed it on my laptop first. So I rebased to Aurora.
I haven’t had any problem with Aurora 41 DX Nvidia Open driver on my PC, it received a couple of 41 updates then 42 yesterday. It works fine.
Rather than trying this convoluted way (and no guarantee the BitTorrent link is still Bazzite 41), I suggest you try with the regular Aurora AMD/Intel ISO, not the NVIDIA ISO. Maybe it’s an NVIDIA driver problem with the installer. If it works, you’ll be able to rebase to the NVIDIA version.