I also have an HP Omen with the i7 CPU. The fact that the i7 CPUs are now being denied the update when previously they were approved is disappointing. I know of a few beta testers that ran Windows 11 just fine during the testing phase with the same processor.
I do not game on my Omen but use it for work, however, Steam came out with a Linux OS for Steam Games that seems to work really well. I am trying to be patient and wait until the end of the year before making any final changes, however, if this issue is not fixed, then like others I will convert my system to Linux and be done with Windows.
We should at least be given the option to do the upgrade and then if it causes a problem with our systems then that is on the user themselves.