Gaming laptop is simply too many compromises.
It’s hot.
It’s loud.
It weights a lot.
Design might be off-putting.
Battery is terrible.
I would just get Legion Go, it’s the most powerful handheld right now, screen is huge. You can always play using GeForce now for full RT 4K 120fps.
What a horrible advice... Yes, some of those downsides can be true, some are mitigated in different laptops, but why recommend lone of the worst windows handhelds out there? Even the Asus ROG Ally performs better and is much more portable. The Steam Deck OLED is a very serious contender too. The streaming capabilities of it are night and day compared to the LCD model. I can stream my main PCs and PS5 to it with no artifacts or discernable lag.
On the downsides:
"It’s hot." It's not about how hot it is, but the heat dissipation being good. Also you can undervolt to lower temps and increase performance
"It’s loud." Not a problem if you're wearing headphones. Also you can use above advice, lower the power profile a tad bit which will decrease fan noise to the 40db range which is barely louder than ambient noise
"It weights a lot." Depends on the laptop, but for the price range the OP is looking at you can get decent specs at under 3kg. Plus, you set a laptop on a desk, I don't think that's a factor.
"Design might be off-putting." That can apply to anything in life, there are 100's of designs and most even allow you to turn off RGB
"Battery is terrible." Not really an important factor, a gaming laptop is used while plugged to the power, unless you're just doing very light gaming. For which the power profile should be set at low, with no fan noise whatsoever and running very cool.