For around 7000 SEK I’d probably focus on getting the best balance between CPU, graphics card and battery instead of chasing “gaming” branding. A lot of cheaper gaming laptops look flashy but have poor cooling or weak screens.
If you want to play games and also use it for school, I’d look for something with at least:
Ryzen 5 or Intel i5
16 GB RAM if possible
RTX 3050 or RTX 4050 graphics
SSD storage only
Lenovo IdeaPad Gaming, ASUS TUF and Acer Nitro are usually pretty decent in that price range, especially if you find a sale. I’d personally avoid the absolute cheapest HP gaming models since they can get noisy and hot.
Also think about what games you actually play. If it’s mostly Minecraft, CS2, Fortnite and schoolwork, you don’t need an extremely powerful laptop. But if you want newer AAA games, 7000 SEK gets tight pretty quickly and buying used can give much more value.