You're unlikely to find something with dedicated graphics for that price, which means gaming will be very limited.
The best you're likely to find would be something with AMD's Vega graphics which are a cut above Intel's mainstream integrated graphics, but are still not a patch on a dedicated GPU.
Something like this has Vega 8 in a 3500U
Buy ASUS 15.6" VivoBook 15 F512DA Laptop (Ryzen 5, 8GB DDR4, 256GB SSD, Radeon Vega 8, Slate Gray) featuring 2.0 GHz AMD Ryzen 5 3500U Quad-Core, 8GB DDR4 | 256GB NVME PCIe M.2 SSD, 15.6" 1920 x 1080 Full HD Display, Integrated AMD Radeon Vega 8 Graphics, microSD Media Card Reader, USB Type-A &...
As a rough indicator of performance, see this article which reviews the Ryzen 5 4500U but also includes the older 3500U in the benchmarks (i.e the CPU in that laptop above).
This is our first review of AMD's Ryzen Mobile 4000 U-series processors, the low power variants intended for slim, light, ultraportable laptops. Our exploration starts with the mid-range Ryzen...
You're dealing with a price range where the hardware isn't intended for gaming, during a pandemic with both escalated demand and supply issues, and also during back to school season.
Although if you get lucky and find something with a GTX graphics card in it in that price range, pounce on it.
Also be aware if you're not already that laptop graphics can't be upgraded unlike in a desktop, so once your laptop's graphics horsepower isn't enough to do what you want them to, you need to buy a while new system to get more gaming performance. That's the nature of laptops and if you need a laptop, you need a laptop, but it's worth being aware of the limitation