This was tested on latest Fedora 43 Kinoite and Chromium Flathub v144.0.7559.109
Make sure to do the OEM unlocking step from the Web installation guide
Your device should have at least 2 GB RAM and 32 GB storage free.
run this command in the terminal:
rpm-ostree install android-tools
wait till it finishes and ask you to type systemctl reboot, type this command in terminal so your devices reboot.
You don't need to run the fwupd command
Install Chromium from Flathub, you can type in terminal flatpak install flathub org.chromium.Chromium to install it quickly.
Launch Chromium and go to the web install (without going into incognito mode), just the normal window. (Ignore flatpak warning and "Flashing as non-root" and "Working around fwupd bugs on Linux distributions" as no longer relevant and Fedora has been working fine)
Then follow the installation guide from here https://grapheneos.org/install/web#booting-into-the-bootloader-interface
Let me if it works too, I don't know if other browsers than Chromium works as flatpak.