It worked! Thank you /e/ developers for making a beautiful installer 
Who wants to try it, please follow GrapheneOS guide (linked ↑) on how to setup your system, so web installer would work. What I mentioned earlier is not enough, for example, Brave also needs Shields feature to be disabled. Best is to follow GrapheneOS guide directly which is comprehensive for every situation.
Improvement suggestions to the installer:
- Copy GrapheneOS guide on how to prepare the system. They include a lot of steps, maybe not everything is necessary, but it is better to have everything in all place just to be safe for people to have good experience, instead of keep failing and debugging things in the forum. Snaps/flatpaks issue should be tested further, maybe finding the cause of problem in forums or in practice and fixed upstream.
- Installer should list how to unlock Fairphone 4 and possible every other phone model where it differs. Now it is unclear what to do on that step as it is a lot more complicated when installer said.
- It was a bit confusing when installation steps started going in loops (repeating configuration steps all over again multiple times), I thought maybe it is not working, but eventually it worked. It could be written in advance that the process will go in loops for a while. Not a super big issue, but still.
- Phone was left in unlocked state at the end. This has to be fixed. If it is complex for this moment, explain the user the situation. As of now, those security dates are highly complex to understand and find out what they are, especially because they are documented wrong. Right now, if I would lock the bootloader after this installation, it would be bircked, as dates don’t match). We documented in comments 1, 2, 4, 5, 8 in this issue: Unable to install on new Fairphone 4 via Easy/web installers, and security patch dates do not match on latest builds - #8 by mnd