Ok - so in order to run 1080p at Ultra with anything over 60-80 frames per second you are gonna need a current gen Video Card. Since the Monitor is "FreeSync" (an AMD technology) sticking with AMD video cards will mean the most compatibility and you the Omen is already AMD anyway so it makes sense to stay AMD.
Even the most recent GTX4070 can't support 1080p Ultra at 240 fps so here goes... but using FreeSync and locking fps at something like 120 (the human eye can't distinguish anything faster than about 60 and 24 is the standard for frame rate at movie theaters) and keeping VSync enabled usually results in the best gaming experience.
You currently have the RX5500 4GB and the newest version is the RX 7900 XTX 20GB which is around $1200 by itself but if you take one step down to the RX 6950 XT (which is actually better than the RX 7900 XT Ultra) then you cut that price in half... they are all here on the same page so you can see the prices: XFX Speedster Merc
...BUT... you current Omen only has a 600W power supply and the 6950 recommends an 800W so without upgrading the power supply you are going to be stuck at the 5000 Series. So you have to upgrade the power supply (the easiest upgrade you will do - plug & play.) And this will get you to RDNA2 and being able to use Ray Tracing.
So in agreement with @BobTheBirdTurd
start with a new M.2 SSD: Samsung 980 Pro
Then 4 x 16GB SDRAM Upgrade: GSkill RipJaw Black
= $170 (you might find something better, but the HyperX RGB that's currently in the Omen is out of stock, and you need to ask him if he cares more about the RGB lightning or ultimate speed cause you save a few bucks not having the lighting on the RAM.)
Then decide if you want to spend ~$115-150 to upgrade the Power Supply: Corsair RM850e
So you can run the $700 RX6950 XT
Total = $845